Call it hanging out. Set up a hang out time with some other friends and invite him. If all goes well, he'll go and have a fun time. Then you can say you had fun and you should do it again! Good luck girlfriend! Go get him! :0)
Try low key first like going to get some coffee or just hanging out at local Barnes n Noble. Ask if he wants to go hang out sometime. See how it goes then either way you've both taken the time to get to know one another.
Don't write a note. I would get creeped out and probably think it was a prank. Just talk to him a couple times then say "hey you wanna go out with me sometime?" And don't wait for him to ask first. It may not happen how you'd like.