There are three basic tones you can use in djembe playing; the bass, open and slap tones. These three different sounds are what all of the various djembe rhythms are built from. Each djembe sound can be mapped to the hand in a way that helps you learn how to play them.
If you think of the djembe notes in terms of their pitch, low (bass), mid (open) and high (slap), they correspond to the different parts of your hand that you use to make these sounds. I'll break this down more as I cover each tone below.
The bass note is played using the palm of your hand. Strike the head somewhere between the center and the edge of the shell. Be sure to focus the hit on the palm of your hand and not the fingers. You can see in the picture that the fingers are not even touching the head.
In djembe playing, the open and slap notes are played very similar, but there are minor variations between the two that achieve different sounds. You'll notice in the picture above, that the knuckles are aligned with the edge of the shell. This is where you want your hand to be when it hits the djembe. Be sure to keep your fingers together and focus the weight of the hit on the bottom portion of your hand where the fingers meet the palm.
The slap is played pretty much like the open tone, except you want to focus the hit on your fingertips. I've heard a few different variations on playing this tone. One says you should arch your hand a little to keep from hitting the djembe head with an open tone. Another says to spread your fingers apart instead of keeping them closed as in the open tone. Still another says to hit the rim of the djembe with your palm first and then hit the djembe head with your fingertips almost like a rimshot. Try playing them all and see which one works for you and most importantly, which one actually produces a different tone for you. These two sounds are probably the hardest to get sounding good because they can be so similar.
Mamady Keita, demonstrates how to play these tones beginning with slap, moving on to open and finishing with bass.
Mike Coletta playing all three sounds. Shows you how to differentiate between open and slap by spreading fingers.