The "go-to" material for a lot of people is something that is inexpensive and easy to make using gelatin and glycerin (and sometimes additional ingredients). It can be used directly or foamed. You can make a big batch of the material and it will keep for quite a while. To use it, you melt as much as you need (including recycles from previous use), pour it into a mold and let it cool (if you foam it, I'm not sure what happens to it if you re-melt it; I'm guessing it would retain some of the bubbles, like a partially foamed material, and you could probably re-foam it).
leigero's answer includes a link that describes a tapioca-based material with gelatin added for strength. One way the author describes using that material is shaping the cool mixture freehand. I haven't previously seen a description of using the gelatin/glycerin material that way, so I'm not aware of how well it would work for that process; it's typically poured into a mold.
If you do an online search on "gelatin prosthetics", there are tons of tutorials, and recipes people have tweaked to their liking. The ratio of gelatin to glycerin varies a little, and some recipes include a little water. The most common additional "active" ingredient is honey or sorbitol. Some people mix in coloring materials to start with something closely matching skin color.
There are several approaches to foaming, if you want to do that. One is to add a few drops of liquid soap and then whip the mixture. Another is to add yeast to the mixture shortly before you use it, which foams pretty quickly in the warm liquid.
Here are a few good links to get you started:
Gelatin/glycerin material also makes excellent molds for casting many kinds of materials; an inexpensive, reusable replacement for silicone. Note, though, that there are mixtures optimized for that purpose. The material optimized for prosthetics is designed to mimic skin characteristics. If you want to use it for creating molds, you'll get better results with a mixture optimized for that purpose.