So, I was up late one night, not being able to sleep when the fire alarm goes off in my apartment building. Everybody slowly marches outside, and after a bit, I ended up having a conversation with one of my neighbours for about fifteen to twenty minutes.

We get the all clear, and we start heading inside. She says we should hangout sometime, shakes my hand (for the second time), I indicate that I'm game, and we say good night.

Now, obviously she has an interest in me (be it for friends or more). Obviously I was stupid and didn't exchange numbers. Not the worst thing to happen in history. I do know which apartment she's in as it came up (discussed where we were in the building).

So, being a rather inexperienced at this -- I didn't start dating until university, and didn't do much dating before I ended up in a seven year relationship. So, here I am, late twenties, and not knowing what to do next.

Should I just go down to her apartment and knock on the door and suggest we go for coffee or something?

UPDATE: Because I know you people like this sort of thing....

We have a winner: http://www.reddit.com/r/seduction/comments/dnvus/we_should_hang_out_sometime_now_what/c11meh1

Not to say the other posters are losers, this is just what happened. I went down there, and she wasn't home, but I came prepared with a note. Basically, it was nice and succinct. I asked her if she was still up for hanging out and left my name/number. She called back after about an hour (a damn long hour, I might add).

Tomorrow evening, we're going for a half hour stroll to a coffee shop that she frequents. I must say that I'm looking forward to it :)