What happens after your first date depends on how the date went and how you handled it at the time. If it was a complete disaster, then the chances are that your date also felt the same way. You may have ended a lukewarm evening with, "Well, I had a great time, and it was nice to meet you, but I don't think we're ideally suited to each other". You can write the date off as a learning experience and move on to the next date.
If the two of you got on really well but there was no chemistry there, then you should still think about swapping addresses and consider whether some of your other single friends might like an introduction. The key thing is to use each date positively and move on. Turn bad experiences into amusing stories, lukewarm experiences into possible potentials for other friends, and fabulous first dates into the start of something new and exciting.