Hi Confused Monkey,
There is a small section in The Foam Book on creating animal puppets starting on page 60. There's also a section on the Foam Book DVD that talks a little about animal puppets. Basically you can use the same technique-- whether it be nip and tuck or three-piece head-- that you would use to make a human puppet. The difference would be in the shape or scale. For instance, a bird puppet might start off as a small three-piece head, but instead of setting the mouth plate into the three piece head, you can make the mouth plate extend out like the shape of a beak and attach separately to the rest of the head.
Also, depending on what your animal puppet is used for it may not need a moving mouth at all. In our touring show Tangle of Tales, one of the stories we tell is the Three Little Pigs. In our production the wolf is a moving mouth puppet, but the pigs are all rod puppets. You can see a photo here on our website: http://www.greysealpuppets.com/OnStageTangle.html
If you have any other questions, please feel free to ask. We want to set you in the right direction!