Wave your hand over them, say Ala Kazam, you’re a balloon!
What they really want: a fun interaction. You're a clown! Just like many other skills clowns use, the intent is not to be the best at that skill (though we always seek to increase our skills). The intent is to use that skill to bring joy and connection in the moment with that person or audience.
Calling this the cheater approach is, well, cheating. If you're bringing joy and connection, the technical means is secondary. But for the purposes of a page on balloon animals, folks assume you will produce an animal (or other creation) from one or more balloons.
The simplest way to produce balloon animals is to... buy mini balloon animals and have them at the ready. Before you guffaw too mightily, know that there is a magic trick whose basic premise is to produce pre-made animals. Smart magician, that one!
Many a clown has amused many a kid with a choice of the following:
You'll of course need to begin by buying some balloons. We list some balloon suppliers, below. Buy more balloons than you anticipate needing to allow for practice and poppage. For many, many designs, you can work with what are called "260" balloons. When inflated fully, they're 2 inches in diamater and 60 inches long. If inflated fully, trying to make most of the previous designs will pop the balloon. What you'll hear in balloon tutorials is to leave a 1 finger tail or a two finger tail or a two inch tail or ... By that, they mean to leave that much balloon uninflated at the end. This allows room for the air to move as you twist the balloon into its designs.
To put air into the balloons, most clowns use a pump, rather than attempting to blow up the balloon by mouth. A simple dual action hand pump will push air with each movement of its handle. Much comedy can occur by "forgetting" to hold onto the end of the balloon while pumping, or letting the balloon go once it has air in it.