"Hi, my name is Marcus Milius. I play harmonica. I got a degree at the University of Southern California, a Bachelor's of Music, in Jazz Studies - Chromatic Harmonica. I play and teach harmonica here in New York City, and I'm happy to show you what I do.
First thing you want to do is train your ear to tell the difference between chords and single notes. For instance, a chord is more than one note, and a single note is just one note. Pucker method - you'll be puckering your lips to get one single note. You'll want to bring the sides of your mouth in, tilt the back of the harmonica up and the front of the harmonica down, and the harmonica will rest on your lower lip and the sides of your mouths will be blocking the adjacent holes. It'll be in the bottom of an oval shape here like this. You'll want to move from side to side to isolate that note until you're sure that you've got it. Tongue blocking - you'll put your tongue on the harmonica and for instance, you'll have your mouth open wide to get about four notes and your tongue will block 3 of them so that you only get one. Typically most people will block on the left side so that they're playing out of the right side of their mouth, but it can be done either way. That will sound like this - tongue off the left side.
Tongue blocking also allows you to add in chords when you'd like to, which you can't do necessarily as well with the pucker method. So, you can take your tongue off the harmonica to get those chords. Which is typical for folk music or Chicago blues style. When you do pucker method, your tongue is free to make articulations like 'ta', 'ti-ka', and 'ti-ka-ta' or any other articulations which allows you to play more staccato. And you can get repeated notes very fast in staccato whereas if you're using tongue blocking your tongue is on the harmonica and you can't make those articulations, so you do that with a [xx] in the back of your throat, like a cough. So both techniques are equally important and used a lot in all styles of music, so I would recommend learning both."