There are four basic sounds, each of which can be played two ways; with the fingertips or top part of the hand, and the thumb or heel of the hand.
The jingle sound is notated with a headless stem. This was the biggest improvement on the old style of notation. The jingles get played a lot as they often act as a ride cymbal. Having no notehead allows us to see clearly where the jingles are being played, and therefore how the drum is moving, but also makes the other notes stand out more clearly. This one looks pretty strange isolated like this, but it will make more sense when you see it in context.
Jingle with fingertips
Jingle with heel
The bass sound is depicted with a standard notehead. To mute it the notehead is placed in parentheses.
Open bass with fingertips
Open bass with thumb
Muted bass with fingertips
Muted bass with thumb
The slap sound is most often played with an open-handed slap, leading with the fingertips. It can also be played leading with the heel but it's more difficult to get clean, sharp slap, so you won't see it that often.
Slap leading with fingers
Slap leading with heel
Here are the various sounds in context. First, the simplest way to play samba on the pandeiro, and the pattern that most people learn first:
The pattern starts with the lower part of the hand and never stops alternating, so the drum just continues back and forth. We can keep this same motion, but add a slap before the open bass sound, emulating a ripique:
One more without having to change directions; add an open bass with the fingertips just before the muted bass sound on beat one:
Now, the first direction change. Technically, in terms of the different tones, this one is the same as the previous example. But here we play the pickup note with the thumb. This is a more traditional way to play, and is also more common on nylon pandeiro. The version above is a more modern way of playing, popularized by players like Marcos Suzano.
Finally, here's a two-bar phrase that incorporates some third surdo language.
In the transcription I am going to post in a few days you'll see a different style of playing with a lot more syncopation that does not require the drum to be in constant motion.