Help with first time meeting a girl?

[979]

Ok so there's this girl in one of my classes i think she's really cute. I've seen her staring at me a couple of times, and I just want to get to know her. We've got this trip for our class assignment and I was thinking of talking to her after the trip is over (it goes for 2 hours to and from our uni).

i don't really have my own phone my brother and I share the same phone and my mom and dad use it as well lol even though they've got their own phones each :o

Should I start talking to her about the classes then ask for her number? or ask to add her on facebook? I also would like some date ideas because I've never dated a girl before. I also am not a very good driver so i can only stick to local places xD

Thanks