Since you guys don't talk, then go and break the ice yourself. Don't wait for him to make the first move because he probably never will. You need to take action into your own hands and start a conversation with him. Waiting for someone to come to usually doesn't result in anything.
I do realize that if you guys haven't talked before, it may seem awkward at first. But just randomly come up to him and be like "hi, my name is blah blah blah..." when he's alone. Once you do it, it's not as awkward as you think it is. If he makes it awkward, then just continue talking as if it wasn't awkward. Important thing is to be yourself and act natural. If you behave naturally and are comfortable with the whole situation, it will make him comfortable too and a lot of that social anxiety would just melt away on its own. If you are stiff, confused, and uncomfortable, it'll be sending him the wrong message that you don't know what you're doing and/or you don't actually want to talk to him.
So what should you talk about with him? Well first off just start with telling your name and a simple greeting like "hello, how are you?" kind of stuff or the "hey, what are you doing?" type of thing. It's straight forward, concise, and it'll force him to actually reply, unless he wants to be rude. If he's going to be rude, then he's not worth your time. If he thinks you are weird for randomly talking to him and gives you "the look", then just shrug, smile, and say something like "I've never had the chance to talk to you before and we've been in the same class for however long, so I just wanted to get to know you." Then after some time, try seeing what he's into and what he likes. You can start talking about those the next time you see him after the initial contact.
If he's shy, he may find this all really weird for the first couple of times. That is perfectly normal. Keep trying to talk to him. He's probably being that way not because he doesn't want to talk to you, but because he doesn't know what to do. He's totally lost that you want to talk to him since you guys have never really talked before. There are a few exceptions like maybe the guy enjoys being a total loner and wants everyone to leave him alone, but those are rare. So even though he's freaked out at first, don't give up until he explicitly tells you to leave him alone. If not, then he'll warm up to you eventually.
Anyway, I hope this helped. Good luck!
