The phrase “what’s up?” is so commonplace that people don’t actually understand the context in which it should be used. I have two responses to this question, which vary based on the situation.
Case 1: I approach someone.
“What’s up?” is appropriate here because they are curious as to the situation at hand. There is a circumstance out of the ordinary that needs to be explained. My response is to explain my situation, and is a nice lead-in to the rest of the conversation.
Case 2: Someone approaches me.
“What’s up?” What’s up? What are they even asking? I haven’t prompted them in any way, so I usually take this to mean “How are you?” People seem surprised when I respond with “alright” or “fine” to this question. Hopefully they are shocked that they didn’t know what they meant to ask, and are grateful for my timely interpretation.