Sounds like its your casual, fun demeanor that attracted her in the first place, so keep that frame of mind going into the date. Don't put too much pressure on yourself else you will continously be thinking about what to do next. I think you're ideas on where to take her are spot on, a drink at a campus bar, throwing around a frisbee in the park, at home to watch a soccer game if she's into it, even just studying together can be fun, avoid lunches and dinners until you get to know her better, they put too much pressure on both of you.
Girls love talking about two things relationships and the unknown avoid anything logical. So make sure you have stories about both that are exciting. Become good at storytelling and embellish a bit to make them interesting. Whenever talking about relationships, even if its about you, talk about it as if its your friend. You can turn her on by speaking about sexual things as long as their in relation to someone else and not you two. ie: my female friend was on a bus and this guy came upto her and said xxx sexual thing, what would you do.
Teasing is key, make sure there is sexual tension by teasing and flirting. ie: slap hands, thumbwrestling, any childhood games are great. Once you catch the vibe that she is looking at you too long, perhaps making nervous gestures around you, just a weird vibe in general, she wants to be kissed. Stroke her hair and than lean in slowly and kiss her. Try and make it spontaneous. Make the first kiss short and sweet and than back off and make it no big deal, than do it again and again and again, each time pushing it further.
As for not understanding what she's saying, if you lead the conversation, you will always understand the thread, so make sure you plan ahead, have topics of conversation ready and think about every possible way the conversation could go. Failing to plan is planning to fail. And if she still talks about nonsense, call her on it in a playful way, she will appreciate it, rather than you pretending to listen, or worse being rude and not listening.
Its easier than you think....now all you have to worry about is.....what to wear!