The diatonic harmonica can be a gorgeous and expressive instrument.  Its standard Richter tuning cleverly allowed players to get the right notes and decent harmonies just by knowing the basic contour of the melody and the difference between tonic and dominant (I and V) harmonies.  However, its design allows for a lot more than that. 

A harmonica in the key of C was meant to play in just that key, in what is now called “straight harp” or first position.  It’s equipped with all the pitches of that major scale (but the top and bottom octaves omit some pitches), and all the blow reeds are tuned to the tonic chord: in the key of C, that’s the pitches C, E, and G.  The draw reeds (the ones that sound when inhaling) play the other notes, which play the dominant harmony, or V chord, which is G in the key of C.  In straight harp playing, if the pitch you want to play fits in the tonic chord, then blow, otherwise draw.  Higher pitches are on the right, lower ones on the left.  If you find the right starting pitch and know the contour and tonic/dominant harmonies, you can work out most simple melodies.  A narrow pucker will let you cleanly play one note at a time, but the beauty of the tuning system is that sloppy playing just leaves you with a decent harmony to accompany your tune.Beyond simple tunes simply played, however, straight harp is often more plain and sterile then is desirable.  (One exception to this is Blues Traveler’s John Popper, who mostly makes up for it in speed and accuracy.)  

A more expressive way of playing is to make use of a side effect of the Richter tuning.  The short version of it is that when the draw reed is higher in pitch than the blow reed on the same hole, and if you use your mouth and tongue to shape the air stream just right, then both reeds start playing together on one pitch somewhere in between.  It’s like gradually transitioning from one pitch to another.  These are called bends.The bendable draw reeds are on the bottom half on the harmonica, the ones that outline a G chord on a C harmonica.  So, if you use the same instrument to play tunes in the key of G, the main pitches of the tune can be embellished with upward scoops at the beginning of notes, falls at the ends, and vibrato in the middles.  

This way of playing is called cross harp, or second position.  It is by far the most common way of playing, and can get you far.  Many players use bends to fake playing through several notes quickly.As natural as it sounds, however, it is difficult to explain exactly how to execute bends or overblows (below).  It all happens inside the mouth, where no one can see well, and even when we can see what’s going on in there, it seems different from how it feels to do it right.  In general, I will say that draw bends (on holes 1-4 and 5) feel like moving a high-arched tongue backward, and blow bends (on holes 8-10) feel like moving the arched tongue forward.  Lower pitches take more motion to bend them than higher pitches.  But ultimately, all of this is going to have to be the result of one’s own experimentation and discovery.

Beyond using bends for ornamentation, this skill can be used to obtain new still pitches.  On any hole, the pitches between the draw reed and blow reed pitches can be played by using the same mouth shape as during bending and freezing at the desired pitch.  For example, hole 1 blowing plays C on a C harmonica, drawing plays D, and draw-bending can yield C-sharp.  On hole 3, however, blowing plays G, drawing plays B, and draw-bending can yield A-flat, A, and B-flat.  With practice, that shape can be remembered and recalled, allowing one to start right on the “bent” pitch.   

This controlled exploitation of bending allows for a lot more to be played on a single harmonica (without changing to harmonicas in different keys), and opens a wider range of timbre, or tone color.  Tones played by bending often sound more throat-like (which is not always desirable) or have character different in some way from unbent tones.  This timbral variety is what makes the diatonic harmonica sound different from chromatic harmonicas, especially when the performer is playing notes outside the key of the harmonica.  Chromatic harmonicas are more like playing straight harp all the time.  (An exception is Stevie Wonder, who plays with an unusually organic tone.)

Bending won’t get you all the notes you can get with a chromatic harmonica, but another technique will (plus one!).  Howard Levy developed a technique that allows this, and he called it overblowing.  This does not mean blowing harder–just differently.  

Overblowing is possible on holes that are draw-bendable.  On those holes, blowing with a mouth shape similar to that of a blow-bend (tongue arched forward) will sound a pitch one half step (one semitone) higher than the draw note.  For example, on hole one on a C harmonica, blowing plays C, draw-bending plays C-sharp, drawing normally plays D, and overblowing plays E-flat, which fills the gap between hole 1 and 2.  This is trickier to get used to doing.  Start with a higher hole like hole 6, which should turn a G (blowing) into a B-flat (overblowing).  Try to blow-bend the G downward, and it should dip a little, then sound raspy, then pop up to B-flat–it isn’t a gradual change like bending.

This will yield every pitch between the high and low extremes except two.  Those two can be played by over-drawing on holes 7 and 9 (on a C harmonica, this is C-sharp and A-flat).  Over-drawing is the most difficult in my opinion, but feels like draw-bending a reed that doesn’t bend that way.  And finally, the highest hole can be over-drawn, playing one note outside the normal range of the harmonica.

Since his time playing with Bèla Fleck and the Flecktones, Howard Levy has reportedly developed the ability to bend over-blown pitches upward, sometimes very far, and also extend the range of draw-bends.  My choice of harmonica is the Hohner Golden Melody, which used to be Levy’s favorite when he was with the Flecktones (which was when I discovered him).  He moved on to customized Marine Bands and other custom built instruments, but I like the tone, maintainability, comfortable feel, and lost cost of the Golden Melody.  Some simple tweaks make overblowing and overdrawing easier, namely closing the gap between the reed and the reed plate around it.  Overblow.com has a thorough discussion of this.

Some harmonicas are made for easier overblowing, for example, the TurboHarp.  ”Turbo Dog,” a.k.a. Dr. Antaki has done some informative scientific research in designing this instrument, and has written some about the science of overblowing.  I like how the molded case feels (I never pick it up upside down because of its asymmetrical and comfortable shape), the tone is noticeably finer than the Golden Melody (it’s more noticeable from the audience), and it does overblow well witout tweaking.  It doesn’t perform significantly better for me than a well-tweaked Golden Melody, however.  Plus, Dr. Antaki gave me a slightly different tuning at my request.  I was getting a low G harmonica, and overblowing low notes is difficult, so I asked him to make the hole 1 draw reed a B-flat (which I can still bend to the usual A and A-flat).

Another instrument that I like playing is the Hohner XB-40, which exploits the bendability of a reed by pairing all twenty normal reeds with an extra set of reeds just so you can bend every note equally well.  I haven’t been able to overblow on it, but I haven’t needed to, either.  Because of this trick, however, the XB-40 sounds somewhat like a chromatic harmonica.  Some reviews of it warn that it’s no easier to get the bent notes in tune than on an ordinary diatonic harmonica.  I would add that the pitches that normally require overblowing or overdrawing are often more difficult to hear in one’s mind and play them in tune right from the start.  When bending to play them, the bend must be accurate; when overblowing to play them, the note more or less snaps into place (albeit usually a little flat, but once you adjust for that, it’s pretty consistent).

Finally, things that will help you learn harmonica is a lot of listening, trying on your own, talking with others, trying on your own, and trying on your own.  For further reading and more people to talk with, try the Harp-L mailing list and archive.  Here is a page of frequently asked questions extracted from the Harp-L archives, which is a good place to go next.