They are just greeting rituals. They don't really mean anything in particular. The greeting people choose is a habit pattern, and a little expression of individuality--like the choice of whether to wear a wristwatch or not. They are just friendly noises.
"How are you?" literally means "are you feeling well," but you don't actually give a real answer, you just say "Fine, thank you, how are you?" Or people may answer with other vague, individualized answers. I know one person who always says "Pretty good, pretty good," another who always says "Fantastic!" and another who always says "Can't complain."
"What's up?" literally means "what things are happening in your life," but it is not a serious question. A friendly, stock, non-answer would be "Not much. What's up with you?" If you want to learn a response, learn that one. Other possibilities are "Life goes on," "Same-old same-old," "Just the usual." The expected answer here is that life has been pleasant but uneventful.
You can actually reply with an illogical answer. If someone says "What's up?" and you say "I'm fine, how are you," nobody is even going to notice that it is illogical. They've given you a friendly greeting, you've given them a friendly response.
I do NOT recommend that you use this--it is MY little personal answer--but an example of how people personalize their answers in silly, small ways. If someone greets me "What's new with you?" I am apt to say "It's been a quiet week in Lake Wobegon." This is because I know most of the people I know would recognize the reference. It is a reference to a radio comedian, Garrison Keillor, who has a regular monolog on his show called "The News from Lake Wobegon." These are gentle, funny stories about an imaginary, remote, small town in Minnesota. The joke is that the "news" ALWAYS begins with the word "It's been a quiet week in Lake Wobegon." By saying this, I'm saying "it's been