Basically, you sign up with Postcrossing, and they will tell you where to send your postcard. You even get to see the person's profile, and find out what kind of postcards they would like. Once your postcard is received, your profile is listed next in the cue to receive a postcard. How exciting! You can start a scrapbook, or just keep the one online.
Here's some we have sent.
And here's some we received!
Hope you try it out, and enjoy it!