There are so many different ways to greet people in English. There is the simple “Hello.” The friendly, “Hi!” or the extremely casual “Hey!” Then you can go to the opposite spectrum and say, “How do you do?” A lot of Americans would look at you funny if said that. Most would probably say in response, “I’m fine, thanks.” However, the correct response is “How do you do?” I guess that shows that Americans don’t use that greeting very much.
Other phrases you can use are, “What’s up?”, “Waz up?” or “How’s it going?” These are used with people you know pretty well. With people you don’t know as well, you can ask, “How are you doing?”
And for saying “Good-bye”, you can say that or, “bye”, “see ya”, “see you later” or to really young kids you can say, “bye-bye.” If you have close friends you can say, “later” or “laters.”
As you can see, there are tons of options in Enlish for greetings and for saying goodbye. Just be careful not to tell your grandma, “Waz up?”