1. My balloons keep popping
First of all, make sure that you are using good quality balloons. While you can work with long balloons that you buy at your local discount or other store - the kind that are made for decorating at a kid's party - these balloons are not designed to take the stress of making balloon animals.
Another tip is to examine your finger nails. If you've recently trimmed your finger nails and the edges are rather sharp, you’ll find that they will tend to pop balloons. Use an emery board or finger nail file to soften the edges of your nails.
2. I run out of balloon when twisting an animal
The recommended uninflated "tips" in the instructions for making balloon animals are only suggestions. If you find that you run out of balloon, simply leave more uninflated tip to accommodate your twisting.
3. The balloon is hard to twist
Two things here. If you find that the balloon is difficult to twist, particularly as you are nearing the completion of a balloon, your balloon has too much air and you’re running out of balloon to twist. In this case, leave a longer "tip" and try and again.
Second, try "burping" the balloon after inflating the balloon. This will leave you with a softer balloon that is easier to twist.
If you have small hands, you may be having a hard time holding and twisting the balloons. In this case, try working with thinner balloons such as the "160" size.
4. The popping bothers me
Despite the precautions listed above, you're going to pop balloons. In many cases, the popping won’t even be your fault because it's not uncommon for balloons to have defects from the factory. Here's what I recommend. When you practice, wear ear-plugs.