How to befriend someone from my uni class

So, I am a university student in my second semester and I haven’t really made any friends in my new city, since I’m rather shy and socially awkward .
This semester there is this guy I see in three of my courses per week. We always sit next to each other, greet and smile at each other every time we meet. As far as I’ve seen I’m the only one he greets and smiles at and he doesn’t really talk to other students or in class, so he might be a little shy aswell.

However, since we both seem to find each other at least somewhat sympathetic I’d really like to try to befriend him, but I don’t know what to do or say without it seeming weird or awkward.

Please give some tips or advice!