The following is coming from a experinced guy standpoint.
Really, when you ask "Will you go out with me?", and they say yes, plan a day like on the weekend, that fits boths of yalls schedule. I remeber when i ask that question to my girl, we didn't go on our first date until like 3 weeks later, because of my schedule. So yea, keep it simple, here's a few first date ideas.
1. Goto a restraunt that has a fun mood, not so much as a romantic mood though.
2. Go see a funny movie.
3. If you decide not to do 1 and 2, cook a dinner at your own home, and rent a movie, or show her movie that you already have.
Anyway, just allow her to feel comfortable around you. Plus it helps if yall had a good solid friendship.