That really depends on what kind of songs you like. If you know a (simple) song that you just can't get out of your head and you are humming it all the time, that would be a perfect start.
For me, one of those is the "Forrest Gump" title song, and i somehow missed it that there
are tabs for it on harptabs.com:
http://www.harptabs.com/song.php?ID=16894.
I usually don't do this (i'm not a very good player), but i uploaded my take on it to Youtube:
[video]http://www.youtube.com/watch?v=Q6l_GGRDxxw[/video]