The hardest part is saying hello
After that it gets easier.
Some people play the eyes game, just try and catch their eye and smile (but not too creepily
). If they like you, then their eyes will linger on you and that's your moment to say hello or let it pass if you don't like their response.
A more direct route, is to just say something situational, telling them you like something they are wearing is a good start or commenting about the party.
You'll find that you want to keep talking to some people and some people you wish you never opened your mouth. Then you have to learn how to escape the conversation, which is a bit harder with some people haha.
The best way to get over this anxiety is exposure, just start talking to people. Expect some of them to go badly, probably the first few people you talk to and then after a while you'll learn the tricks.
As a disclaimer, I don't do any of this because I hate small talk. I'm introverted and I'm going to say something that interests me (usually neuro* related) and if they look at me like "wtf" then I just smile and move on