Sorry if it's a trivial question, but when someone uses what's up as a greeting I have no idea what they want to hear. What are the possible answers and what does this question mean exactly?
“What’s up?” is a greeting whose meaning is mostly irrelevant in that the asker doesn’t want an answer to the literal question which means something like “What is new?” or “What’s happening (right now/in your life)?”.
The simplest response if you don’t have information you want to share immediately with the asker is probably just to say something like “not much”, “not too much”, or “hey (man/dude)”. If you’re offered “what’s up” in response to a greeting of your own, you should read it as a request for you to proceed to the content part of what you want to talk about.
That is an expression that has about as much meaningfulness as "How are you?" or "How's it going?" All, including "What's up?" are used as greetings. Now, each can be taken literally where someone may want to truly know "how you are", particularly if you've been sick, for instance, but all those terms are very commonly used along with the traditional greeting words, "Hi, "Hello", "Hey".
What's up? - "Not much, how about with you?"
How are you? - "Fine, and you?"
How's it going? - "OK. How's it going with you?"
You can respond using this (pick one):
Thank God, I am doing well (or: Unfortunately, I'm not doing so well today, or: Everything is in order, or: Not much, et al.).
I think it is acceptable as well to reply back with the same greeting:
How are you doing (today/tonight/this morning/this afternoon/this evening)?