Embouchures
The embouchure (ahm' ba sure) is the method of applying the lips and tongue to the mouthpiece of a wind instrument, like the harmonica! If you are just learning to play I recommend you start with the Lip Block.
Lip Block
Lip Block is a variant of the pucker (see below), it's also called lipping. Tilt the harmonica up at the back about 30 to 45 degrees, and open your mouth pretty wide, enough to cover about 3 holes, with your upper lip about 1/2 to 2/3 of the way over the top cover. Let the harmonica nestle into your lower lip. What happens is that quite naturally, without really trying and without forcing it, the lower lip blocks the 2 side holes and lets the center hole sound cleanly.
The open mouth position helps improve your resonance, which in turn helps in getting bends correctly, and improves your overall tone. The harmonica needs to be well in your mouth... Don't be shy! You can't just peck it with puckered lips and make it work right. You should be relaxed, without tightening your lips or pinching in your cheeks.
Pucker
The pucker style has the lips pursed and pushed out, and the harmonica is positioned deep back into the mouth (but not are far back as for tongue blocking or U-blocking. See below). The air stream is "directed through the pucker to one hole".
(Note: This is as described in many beginning harmonica books, ala John Gindick's. In my opinion, the pucker does not direct the air stream through the hole so much as the deep position of the harmonica in the mouth brings the lips into contact with the side holes not to be played.)
Note: I believe that for experienced players the pucker and lip block evolve so as to become nearly indistinguishable. In my opinion, it is easier to reach this "pucker/block" embouchure starting with the lip block than with the "pucker" mental image.
Tongue Block
In the Tongue Block the mouth is opened to cover 3 or more holes, and the tongue blocks the holes that are not intended to sound. The tongue block pretty much must be used for octave and split interval play . Tongue blocking also facilitates various harmonica playing techniques and effects, such as "slaps" and "flutters".
The tongue normally blocks the holes on the left and leaves a single note on the right unblocked to sound, but the tongue can also block holes on the right leaving a single note on the left to play. It's best to learn to block and play on both sides to facilitate quick jumps and easy access to holes on both ends of the harmonica.
Classic harmonica blues players mostly played use the tongue block. technique Some of the bends sound so good in tongue block.. even from someone who normally does not play using tongue block. I think, though, that above hole 6 tongue block is not the preferred embouchure.
U-Block
A variant of the Tongue Block is the U-Block, where the tongue is (normally) rolled into a "U" shape, though the tightness of the curve varies a lot from player to player. The tip of the tongue is placed just beneath the hole to be played or even down onto the lower cover. The mouth is open to cover about 3 holes, and the tongue curves up, or is pushed up to block the left and right holes.
Best Choice?
All bends and overblows/overdraws are available using any of these embouchures, though to me the tongue block and U-block are not a good choice for overbends. There is no clear evidence of which I am aware that any embouchure allows faster or cleaner play than any other. The consensus best approach is to learn them all and use the ones you like. I prefer the lip block, especially since I've incorporated overblows through out my play. Since that's what I like, that's what I'll recommend.
Also note: It is possible to "pucker/block" out of either corner of the mouth, and it is possible to lip block on either side of a single hole to be played. These modifications to the "standard" embouchures can add speed and accuracy since less harmonica/head movement is required to jump to a non-contiguous note. For the pucker/block, the harmonica is "twisted" from side to side to bring either corner of the mouth into play. For the tongue block, the tongue is moved left or right to cover/expose the proper notes. For U-blocking, the tongue can be moved from side to side to select individual notes with little or no movement of the harmonica relative to the mouth.