JustWuzzle... Listen to MartyMcFly. And as long as you don't go up to some random guy, it won't be that weird. Just be friendly with them for a while, and then simply ask "what are you up to later?"
I've done this before when I went to the Park District to play basketball at the "open gym" times. I played a game with a group of friends that were there, asked them what they were doing, if they were going out, and I ended up meeting up with them at a bar. Stayed in contact for a while. It's not that hard.
Key is to come off as a fun guy, and becoming their friends won't even take effort. If you approach the situation really awkward, they are gonna want no part of it.