how do I approach people?

 Basically what the title says. I (21f) have always been a very introverted and rather awkward person. Ever since starting uni, I was only able to make one genuine friend. I just generally don’t really know how to talk to people/actually get to know them. Like yeah ill have small talk here and there but how do I ACTUALLY become their friend with someone. 

Asking because; 

There is this really cute guy in my art history class. The class has only 5 people in it, so the discussions are always very chill and just basically us talking casually about the given topic (animal studies). He always says such smart things, one would say that it's noticeable he actually THINKS before speaking. Never once did I get the feeling of him trying to mansplain something. Sometimes, when he says something in the discussion, I'll try picking up on it just so he knows we agree on a lot of things. So, small interactions are already happening, but kinda only cause we have to...

So my question is; how do I approach him without making myself look like an idiot???