Wow, I thought this thread had died, but since it's back I'll try to put some closure on it.

I appreciate Old Timer's comments because they reflect what I've been able to gather from reading legal stuff, corresponding with ASCAP, and talking to people in my area who perform locally for small amounts of money.

The bottom line is that you should get permission before using someone's music, and that is done by writing a letter or calling, usually to the publisher. It was suggested that you provide your own "I give permission" form letter for someone to sign and send back to you in the stamped, self-addressed envelope you provide. However, copyright laws exist to protect artists from losing money because someone else is making money off their work. If I sing a song at my church's coffeehouse, the artist is not losing any money (and in at least one case someone bought the artist's CD because they liked the song I sang). I should ask permission first, and I could get sued if I don't, but I suspect the publishers and copyright owners have better things to do than track me down if I don't.

Most of us want to do the right thing, so it's helpful to have the basic rules and the "real life" context. Thanks to everyone who's contributed to this thread.