Shirk can be in Ruboobiyyah, Asma was-Sifaat, and Uluhiyyah.
Shirk in Ruboobiyyah
There are two kinds:
1] Shirk Ta'teel: Denying Allah
An example of one who committed this type of shirk is Fir'awn.
قَالَ فِرْعَوْنُ وَمَا رَبُّ الْعَالَمِينَ
"Fir'aun (Pharaoh) said: "And what is the Lord of the 'Alamîn (mankind, jinns and all that exists)?" [ash-Shuraa 26:23]
...وَقَالَ فِرْعَوْنُ يَا أَيُّهَا الْمَلَأُ مَا عَلِمْتُ لَكُم مِّنْ إِلَٰهٍ غَيْرِي
"Fir'aun (Pharaoh) said: "O chiefs! I know not that you have an ilâh (a god) other than me.." [al-Qasas 28:38]
فَقَالَ أَنَا رَبُّكُمُ الْأَعْلَىٰ
"And proclaimed: 'I (Pharaoh) am your Lord the Highest.'" [an-Naziat 79:24]
This resembles the beliefs of those who merge philosophy with Islam and claim that the universe was old and created itself. By this they deny the existence of Allah (عز وجل) and it is of the biggest of Kufr. With this belief one:
- Denies Allah
- Denies angels
- Denies the books because they believe the books came from the human mind itself
- Denies messengers because it is a trait not from Allah
- Denies prohibitions and ordiantions
- Denies the hereafter
A prime example of this is Ibn al-Arabi who believed in the universality of the world. In his poem he says "Al-abd rabb warabbu abd fa ya layta shi'ree man huwal ma'bood.." Meaning, "The slave is the lord and the lord is the slave so how I wish I that I knew who was to be worshipped."
2] Shirk In Associating Partners with Allah.
Examples:
The Majoos worship two lords; one for good and one for bad, light and dark
The Christians worship three lords.
The Sa'bah worship the stars in sky because they believe they control the world.
The grave worshippers believe the souls in the graves have control in the universe.
(Example of grave worshipper) - 
Shirk in Asma and Sifat
There are two kinds:
1] Shirk in the Names
This is done by taking the names of Allah and applying the name to other things they worship. For example, the name 'Uza from al-Azeez, Manat from al-Manat, al-Lat from Allah.
2] Shirk Al Mushabbihah
This is done when one compares Allah's attributes to the attributes of people. For example, saying that Allah's hands are like mine, or Allah has hearing like mine. The Shia'a are guilty of this shirk. Radical Shia'a such as the albaniyyah, alsalimiyyah, who believe that Allah comes on mount Arafat on a camel and gives lectures.
Whoever worships something like that worships statues concocted in his brain through the faculties of his imagination.
Shirk in Uloohiyyah
This is the big shirk, believing that there is a partner with Allah (عز وجل) in Ibadah or by giving Ibadah to other than Allah (عز وجل).
(For an example, see the picture below of an Ismai'li Shia'a bowing before a man [who, by the way, happens to be picking his teeth--someone ought to teach this guru some manners] )
This comes in numerous forms with many examples we must know:
1) First, Shirk in Love.
This means taking partners in the love of Allah. Meaning, you love that thing like your love for Allah.
وَمِنَ النَّاسِ مَن يَتَّخِذُ مِن دُونِ اللَّهِ أَندَادًا يُحِبُّونَهُمْ كَحُبِّ اللَّهِ ۖ وَالَّذِينَ آمَنُوا أَشَدُّ حُبًّا لِّلَّهِ ۗ وَلَوْ يَرَى الَّذِينَ ظَلَمُوا إِذْ يَرَوْنَ الْعَذَابَ أَنَّ الْقُوَّةَ لِلَّهِ جَمِيعًا وَأَنَّ اللَّهَ شَدِيدُ الْعَذَابِ
"And of mankind are some who take (for worship) others besides Allâh as rivals (to Allâh). They love them as they love Allâh. But those who believe, love Allâh more (than anything else). If only, those who do wrong could see, when they will see the torment, that all power belongs to Allâh and that Allâh is Severe in punishment." [al-Baqarah 2:165]
For those who committed shirk by making others equal to Allah (عز وجل), this is what they say in hellfire:
تَاللَّهِ إِن كُنَّا لَفِي ضَلَالٍ مُّبِينٍ
"By Allâh, we were truly in a manifest error.." [ash-Shuraa 26:97]
Every love has hope and fear and we know that the more love and fear there is the more it has control of the heart. Shirk in love here refers to that kind of love that worships. It is a love that has humility, hope and fear directed at that whom you love.
Ibadah has 2 pillars:
A] peak of love
B] "thul" or humility-submission to Allah
Both must be restricted according to the Qur'an and the Sunnah. The peak of love requires one to abide by Allah's commandments while the peak of humility to Alllah (عز وجل) is to stay away from that which is prohibited.
This is the mahabbah of Ibadah, the love that concerns worship.
Other kinds of love:
Natural love: The love of water or the love of food for one who is thirsty or hungry for food
Love and mercy: The love of a parent to the child
Love that has respect: The love of a son to the father
Love of friendship: The love between friends who meet
These all occur naturally.
2) Second, Shirk in Fear
This means that there is fear from a person from other than Allah in that some harm will happen by that other's will and might. This goes against what Allah (عز وجل) has stated:
...فَلَا تَخْشَوُا النَّاسَ وَاخْشَوْنِ...
"..Therefore fear not men but fear Me.." [al-Ma'idah 5:44]
إِنَّمَا ذَٰلِكُمُ الشَّيْطَانُ يُخَوِّفُ أَوْلِيَاءَهُ فَلَا تَخَافُوهُمْ وَخَافُونِ إِن كُنتُم مُّؤْمِنِينَ
It is only Shaitân (Satan) that suggests to you the fear of his Auliyâ' [supporters and friends (polytheists, disbelievers in the Oneness of Allâh and in His Messenger, Muhammad SAW)], so fear them not, but fear Me, if you are (true) believers. [ali-Imran 3:175]
...فَإِيَّايَ فَارْهَبُونِ...
"Then, fear Me much" [an-Nahl 16:51]
Kinds of Fear:
a) The first kind of fear is fear from other than Allah in that which only Allah (عز وجل) can inflict upon the person such as illness, and poverty.
For instance, if one believes he will be killed by mere will and not by other physical means. Some more examples are, believing that a dead person can put a curse on you to get fired, stop your paychecks from coming, or to stop you from entering jannah or can place you in hell.
This is ibadah of fear, and it is also called secret fear because there is no reason for someone to fear the even remote chance that a dead person can prevent one from receiving his paycheck. It is something that is not apparent such as knife held against someone's chest. This is what the mushrikeen believed of their statues, non living objects able to bring upon them some sort of infliction.
This constitutes major shirk because these capabilities are reserved for Allah alone.
Sulayman bin Muhammad bin Abdul-Wahab noted an example of this in Kitab at-Tawheed. He said during his time someone had borrowed and dealt in business with the people of an area in the Arabian peninsula. This man became bankrupt and was unable to pay back what he had borrowed. The townsmen ran after him and he consequently went to a grave and said "I will call and get this sacred person in this grave to harm and curse you." Thus the people left him alone thinking of the harm that dead person will bring to them.
b) the second kind of fear is to fear performing jihad or to ordain the good and forbid the evil without valid reason except the fear of people. This is haram. Allah (عز وجل) revealed :
إِنَّمَا ذَٰلِكُمُ الشَّيْطَانُ يُخَوِّفُ أَوْلِيَاءَهُ فَلَا تَخَافُوهُمْ وَخَافُونِ إِن كُنتُم مُّؤْمِنِينَ
"It is only the devil who would make (men) fear his partisans. Fear them not; fear Me, if you are true believers." [ali-Imran 3:175]
In the Musnad of Imam Ahmad there is a hadith where Allah (عز وجل) will ask someone on the day of judgment "Why did you not ordain the good and forbid the evil?" He will say "Oh Allah I feared people." Allah (عز وجل) will say "You should of feared me."
c) The third fear is fear of the punishment of Allah (عز وجل).
وَلِمَنْ خَافَ مَقَامَ رَبِّهِ جَنَّتَانِ
"But for him who fears the standing before his Lord there are two gardens." [ar-Rahman 55:46]
يُوفُونَ بِالنَّذْرِ وَيَخَافُونَ يَوْمًا كَانَ شَرُّهُ مُسْتَطِيرًا
"They (are those who) fulfill (their) vows, and they fear a Day whose evil will be wide-spreading." [al-Insan 76:7]
Ibn Taymiyyah said this fear is praised unless someone goes beyond bounds in it then that will lead to him to abandon the mercy of Allah (عز وجل).
d) The fourth kind of fear is natural fear.
This is something that Allah (عز وجل) equipped us with. It may be called the "flight-or-fight" response where we react to certain very apparent fears in front of us. For instance, it is natural to have a fear of a lion in the same room, a fear of a snake in a forest you are walking in, a fear of an oppressor who might torture you, or even a fear of your employer not giving you your paycheck.
All of these constitute the fear of Musa (عليه السلام) that prompted him to leave the town of the Pharaoh after he killed a man from the tribe of the Pharaoh.
(٢١)فَخَرَجَ مِنْهَا خَائِفًا يَتَرَقَّبُ ۖ قَالَ رَبِّ نَجِّنِي مِنَ الْقَوْمِ الظَّالِمِينَ وَجَاءَ رَجُلٌ مِّنْ أَقْصَى الْمَدِينَةِ يَسْعَىٰ قَالَ يَا مُوسَىٰ إِنَّ الْمَلَأَ يَأْتَمِرُونَ بِكَ لِيَقْتُلُوكَ فَاخْرُجْ إِنِّي لَكَ مِنَ النَّاصِحِينَ(٢٠)
"And there came a man running, from the farthest end of the city. He said: "O Mûsa (Moses)! Verily, the chiefs are taking counsel together about you, to kill you, so escape. Truly, I am to you of those who give sincere advice. So he escaped from there, looking about in a state of fear. He said: "My Lord! Save me from the people who are Zâlimûn (polytheists and wrong-doers)!" [al-Qasas 28:20-21]
What must be noted here is that although it is not a shirk form of fear here, the more ones Iman is stronger the more fearful he is of Allah (عز وجل), while the least he is fearful of other creations even if certain circumstances may be brought upon with that creation's means.
3) Shirk in Rajaa' - hope
This pertains to shirk in having hope in other than Allah in that which only Allah (عز وجل) can facilitate.
For example, those who have hope in the dead by calling on the dead to do good for them or to refrain them from doing bad to them. This applies to someone who is not around as well. For example, to call on one's sheikh who is ten thousand miles away to aid him in his problem, "Oh sheikh so and so, please facilitate food for my son's waleemah!"
On the other hand, if there is hope in something that is physically apparent this is not shirk.
The raja of Ibadah has conditions, of them are: to be low, to be humble and to have humility in that one you have hope in. This can also be referred to as secret hope, such as hoping for victory against one's enemies or hope to have a blessed life. Likewise when one hopes that a mechanic fixes one's car or that one is given a loan, these are not shirk.
Love (Hub), Hope (Rajaa), and Fear (Khawf)
All of these three are contained in Surah al-Fatiha:
الْحَمْدُ لِلَّهِ رَبِّ الْعَالَمِينَ
"All the praises and thanks be to Allâh, the Lord of the 'Alamîn (mankind, jinns and all that exists)." [al-Fatiha 1:2]
This ayah indicates that we should place our love of Allah in praise and gratitude for Him as His dominion is all of His creations.
الرَّحْمَٰنِ الرَّحِيمِ
"The Most Beneficent, the Most Merciful." [al-Fatiha 1:3]
This ayah tells us to place our hope in Allah for His beneficence is unmatched and His mercy is endless.
مَالِكِ يَوْمِ الدِّينِ
"The Only Owner (and the Only Ruling Judge) of the Day of Recompense (i.e. the Day of Resurrection). [al-Fatiha 1:4]
We fear Allah as that inevitable day when our books will be taken into account and it is only from Allah that we will be judged.
To have love for Allah (عز وجل) alone is from the Sufi's. They believe that to have love of Allah (عز وجل) alone is the key to paradise, that we should not even love Jannah or love to acquire a place in Jannah because it pollutes our love of Allah (عز وجل). They claim that to do actions of good deeds for the sake of Allah (عز وجل) should never be motivated by fear because anything motivated by fear lacks sincerity. But this is from falsehood because Allah (عز وجل) Himself commands us to fear Him and to hope in His reward in the Hereafter. (al-Ghazali's al-Maqsad al-Asna fi sharh asma-Allah al-Husna)
Sufis say: "I don't worship due to fear of Him but love…."
If one worships Allah (عز وجل) with khawf (fear) by itself, this is from the belief of the Haroori.
If one worships Allah (عز وجل) with rajaa (hope) by itself, this is from the belief of the murj'i.
If one worships Allah (عز وجل) with all three - love, hope and fear, then this is from the belief of Ahl as-Sunnah wal-Jama'ah.
4) Shirk in Dua'a
Anyone who asks other than Allah (عز وجل) that which only Allah (عز وجل) can give is a mushrik, and Allah (عز وجل) called this shirk.
فَإِذَا رَكِبُوا فِي الْفُلْكِ دَعَوُا اللَّهَ مُخْلِصِينَ لَهُ الدِّينَ فَلَمَّا نَجَّاهُمْ إِلَى الْبَرِّ إِذَا هُمْ يُشْرِكُونَ
"And when they embark on a ship, they invoke Allâh, making their Faith pure for Him only, but when He brings them safely to land, behold, they give a share of their worship to others." [al-'Ankabut 29:65]
Allah (عز وجل) talks about mushrikeen:
وَأَنَّ الْمَسَاجِدَ لِلَّهِ فَلَا تَدْعُوا مَعَ اللَّهِ أَحَدًا
"And the mosques are for Allâh (Alone), so invoke not anyone along with Allâh." [al-Jinn 72:18]
وَلَا تَدْعُ مِن دُونِ اللَّهِ مَا لَا يَنفَعُكَ وَلَا يَضُرُّكَ ۖ فَإِن فَعَلْتَ فَإِنَّكَ إِذًا مِّنَ الظَّالِمِينَ
"And invoke not besides Allâh, any that will neither profit you, nor hurt you, but if (in case) you did so, you shall certainly be one of the Zâlimûn (polytheists and wrong-doers)." [Yunus 10:106]
وَالَّذِينَ تَدْعُونَ مِن دُونِهِ مَا يَمْلِكُونَ مِن قِطْمِيرٍ...
"And those, whom you invoke or call upon instead of Him, own not even a Qitmîr (the thin membrane over the datestone)." [al-Fatir 35:13]
Allah (عز وجل) called it kufr.
وَمَن يَدْعُ مَعَ اللَّهِ إِلَٰهًا آخَرَ لَا بُرْهَانَ لَهُ بِهِ فَإِنَّمَا حِسَابُهُ عِندَ رَبِّهِ ۚ إِنَّهُ لَا يُفْلِحُ الْكَافِرُونَ
"And whoever invokes (or worships), besides Allâh, any other ilâh (god), of whom he has no proof, then his reckoning is only with his Lord. Surely! Al-Kâfirûn (the disbelievers in Allâh and in the Oneness of Allâh, polytheists, pagans, idolaters, etc.) will not be successful." [al-Mu'minun 23:117]
Allah (عز وجل) called them liars and kafiroon.
أَلَا لِلَّهِ الدِّينُ الْخَالِصُ ۚ وَالَّذِينَ اتَّخَذُوا مِن دُونِهِ أَوْلِيَاءَ مَا نَعْبُدُهُمْ إِلَّا لِيُقَرِّبُونَا إِلَى اللَّهِ زُلْفَىٰ إِنَّ اللَّهَ يَحْكُمُ بَيْنَهُمْ فِي مَا هُمْ فِيهِ يَخْتَلِفُونَ ۗ إِنَّ اللَّهَ لَا يَهْدِي مَنْ هُوَ كَاذِبٌ كَفَّارٌ
"Surely, the religion (i.e. the worship and the obedience) is for Allâh only. And those who take Auliyâ' (protectors and helpers) besides Him (say): "We worship them only that they may bring us near to Allâh." Verily, Allâh will judge between them concerning that wherein they differ. Truly, Allâh guides not him who is a liar, and a disbeliever." [az-Zumar 39:3]
Allah (عز وجل) has shown us that the one a person chooses to call upon besides Allah (عز وجل) cannot help that person in anything. The people who commit shirk have nothing, not even a thin skin that surrounds the date seed.
This kind of shirk has become popular and the mushrikeen of the past and present fall into the same trap.
Today, it is common to find by grave yards people uttering words such as "Oh so and so, give me such and such." They ask for shifa'a (intercession) or they ask for aid in uplifting their misery. Whoever does this is a mushrik kafir for that person has committed shirk akbar.
Some common dua'a of those who commit shirk in their dua'a is saying "Madad, madad Ya Hussein", Ya ibn Alwan, Ya Nafseesah, Ya Abdul-Qadir Jaylani. Ya Dasooki, Ya badawi, etc. Meaning, "more strength and power oh Hussein" and so on.
If one calls on a living person to do something within his human capabilities it is permissible. For instance, asking a close friend to fix a car, or for a loan, or to be rescued from some apparent mishap, these are all acceptable. They are acceptable because the person who can help the other is alive, is capable of helping and the means of being helped and helping is apparent.