So. The harmonIca is one of the easiest instruments to play, it sounds really cool, and can be used for a variety of musical styles. All right, maybe not too many musical styles, but it's fun to play anyway. So. Here we go.
Step 1: Types of Harmonicas
Chromatic: These are fancy harmonicas. They have a little button on the side. When you press this button, whatever note you are playing moves up a half step. This allows you to play every note in the musical scale, a chromatic scale. Although they offer more versatility, they are often harder to play, especially if you are trying to bend. Not recommended for blues.
Tremolo and Octave Harmonicas: These harmonicas have a double row of holes. On a tremolo, the notes are tuned slightly apart, but almost the same, creating a cool "tremolo" vibrating effect. On an octave harmonica, the notes are tuned an octave (8 notes) apart, creating a fuller sound. Compare to a 12-string guitar. Both are sort of rarely used.
Special tunings: Some harmonicas come with different scales like minor scales and scales made for playing in more than one key.
Bottom Line: Start with a diatonic harmonica, preferably in the key of C (as this is the easiest key to understand).
Here are some pictures of each type.