There are three basic twists to know when you start balloon twisting. The first two most basic ones are the loop twist and lock twist, followed by the pinch twist, which you’ll eventually want to learn. I may post some pictures of them and describe them at some point, but I found the below web site does a pretty good job of illustrating them.

The lock twist, loop twist, and pinch twist are the first three listed, followed by some more advanced twists.

Check them out here.