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.
Balloon twisting is sometimes harder to do than it looks, but it might not be you! It might the balloons you are using.
The balloons you find at the toy store or local store are often pretty old and not so high quality. Professional balloon artists use high quality balloons, which are much less likely to pop and just easier to manipulate in general.
I’ve always used Qualatex balloons (in my limited experience) and they seem to be used by many professionals. Bellatex is the other major brand. If you know me, feel free to just ask me for some balloons and to borrow a pump, if you want to try it out. I usually have more than enough balloons. (The Qualatex bags come in 100 count and 250 count.)