I had a special request from Adrienne, a recent law school graduate, for more information on how to play the harmonica. I don't know, but I'll find out!
First, what type of harmonica do you have and/or want to learn how to play? Is it diatonic? This is most common, and you can play a full 7-note major scale in the key of the harmonica. Make sure, though -- it could also be chromatic, tremolo, octave tuned, special tuned...or something else entirely. This post'll focus on diatonics, in any case.
First, hold the harmonica with your hands on either side--- it has numbers on the top that you want to be able to see as you're playing. Don't cup it, pinch it. (I have a friend who would say, "That's what she said!" after such a statement). I guess you get fancy with the way you hold it (a la Blues Traveler guy, John Popper) later, when you're better. Let's not get over-eager, Adrienne!
Second, I feel obligated to tell you that you have to be a really good breather to play the harmonica. If you're dead, this just isn't going to work out. For those of us who are alive, playing the harmonica is very good for your lungs -- you have to have extremely good breath control to blow air in AND to suck it out. (That's what she said?) Here's a good article on the breath control required.
Music for the harmonica is generally written in tab form, so they'll give you the numbers you're supposed to blow (air out), signaled by the number and an up arrow, or draw (suck air in), signaled by the number and a down arrow. Go to one note and blow and draw -just fool around a little. You'll be able to hear that it sounds like multiple notes or a chord. To play one note at a time, you should experiment with a pucker formation that's kind of like imitating a fish (and not kissing your grandmother). Put the harmonica in your lips, not on them, over the desired note hole and you should be able to get to a one-note sound. Here's more on the pucker method (including a sample song for beginners to try out).
When you want to start playing more songs, here are a few you can try playing by number. There is also the play by color method, if you want to give that a shot, but the the playing by number is most common.
Here are some videos and more resources:
Monkeysee - how to play harmonica
Bunch of videos
Maybe I'll start playing harmonica at T stations...but where will people put the tips? Harmonica cases are a little small...