Ideas in how to get to know your crush better without making things awkward?

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I'm interested in a guy, but I don't know how to approach him. We're in college and we don't have common friends. I only have him for one class. He comes in right when class starts and leaves right after. I can't talk to him during class. I really want to get to know him better, but I find it difficult finding a way to do it smoothly without literally going up to him which I think is awkward. I've only had one chance to talk to him, so I guess I've broken the ice but that's about it. I've never pursued a guy before because I'm too shy to do it and plus I feel like it's too bold of a move for a girl to do, but I want to do something different this time. Please help!! What should I do, and ideas or advice?

I know he has an instagram account, but I think it would be too weird to add him? I don't want him thinking "oh wow she searched me and added me, I didn't even know she knew my name" type of deal. I'm trying to make it as less awkward as possible