<human>: I [22F] moved into a new apartment in an entirely new city for graduate school this summer. Since then, I've seen this guy [22ish M] several times in the elevator in our apartment complex. Each time we've made small talk and seemed to hit it off well (you know, as far as you can tell with strangers). He's super attractive, seems sweet, and is a grad student at my school in a different program. Today I introduced myself and we exchanged first names. 

How do I progress this further? I've never dated someone that I wasn't very good friends with already, so this is a new situation for me. Next time I see him around can I just say something like "Hey, I hope this isn't too weird, do you want to get coffee sometime?" Is there any better way to handle this, given that we're basically strangers? Should I just grow some lady balls and ask him out directly?

Summarize the given text in a few sentences.
<bot>: How do I [22F] go from random elevator girl to a date with cute grad student [22M]?