Inflate a pencil balloon and seal it by tying a knot at the end. Leave about an inch uninflated at the end so the air can go somewhere once you start twisting.
Hold one end of the balloon and section off a small "bubble" by pinching and twisting the balloon, making an air pocket that's separated from the rest of the balloon.
Add another bubble to the chain by holding the one you just made in Step 2 and twisting off another small section right next to it. Create as many bubbles as you want from your balloon. Keep in mind that different balloon animals may require a different number of bubbles, so plan accordingly.
Connect the ends of your chain together by twisting the pinched spaces between two of the bubbles together.