The first two are used to ask how a person is feeling; the last one is used to ask a person what they're doing at the moment.

You should also know that these can just be common ways of saying "Hi" or acknowledging that someone is there. If I were to talk into a room and see a friend for the first time that day, I might say "How's it going?", "whats up?", "whats going on?", "how (are) you doing?", Or "how are you?" - any of these I could say in passing, and I would expect the other person to just give a casual "nothing", or "doing OK". If they REALLY give me a detailed answer, I would be surprised !! They can be used if you want a detailed answer - but to know the difference, it would be the tone of the words the questions was asked, and the relationship between the two people.

As Tom mentioned, it is important to consider that "How are you (doing)?" often just means that the speaker is acknowledging your presence. That means it is phatic communication, or communication only for social purposes. This can be a confusing cultural reality for someone who speaks English well but doesn't know not to take the question too literally. Outside of North America there are some alternative phrases used to perform the same function. In England "(Are) you alright?" is the most popular one. This one is confusing for a North American, as to us that question indicates that the person asking it believes that something is wrong with us.