It feels like I'm in middle-school >.> What do?

So this is my first year of undergraduate studies. Coming from a highschool with <1000 people to a campus with over 40,000, things are a tad different. One thing is how many more people there are, including lgbt people it seems.

As I grew up in a small town I basically have 0 experience with anything dating. Most of my friends couldn't say anything about dating members of the same gender, so why not ask this forum?

Monday I went to my math prof for help and this guy in my class, named Tim, happened to go too. As we were leaving the building we I struck up conversation. We walked away from the building towards our destinations until we came upon a fork in the road. We ended up standing there for about an hour just talking. So I asked if he wanted to go get coffee, and he said yes. I bought him coffee and we sat for about another hour and talked. It was very interesting conversation, and he is very smart. I don't know if that sounds date-ish or anything, regardless, based upon certain things he said I suspect he's gay, but have no idea what to do next, lol. Should I just ask if he wants to hang out, and then after that ask him out for a date? What do I even do? Lol, just coffee again?

I have no idea how to proceed.