If you are a beginner when it comes to using prismacolor pencils, try experimenting with different colors to get a "feel" over the whole technique. One of the best ways to learn quickly is to just doodle around with and adding layers of colors over each other to see how they all blend in.
One of the big advantage the prismacolor pencils has compared to many other color-pencils is that they work extremely well when it comes to blending different colors with each other. Say you want to go from very bright yellow to very dark red, to do this you just use different shades of red, orange and yellow. Another great tool that you usually get when buying prismacolors is the "blender-pencil", this is a non-color pencil, it works as a blender. Great tool, especially when you want to blend in small details like the fur of an animal.
To start out on a prismacolor animal drawing, I would suggest that you draw the basic lines of the animal very lightly with a normal pencil. Be careful not to draw hard lines, because this can really mess up the drawing later on. Then with when you feel satisfied with the general proportions of the drawing, you erase little by little the pencil lines, and replace them with a prismacolor pencil, still draw very lightly the animal's proportions.
Then start adding the colors lightly, I usually do a small part of the animal, and then just complete that part, before I move on to the next part of the animal, instead of trying to color the whole animal drawing at once.
One good tip I got from a great artist was to add many layers lightly until you get the color you wish for, and then use the "blender-pencil" to blend all the layers into one layer.
Hopefully this will help you improve your animal drawings done with prismacolors! And remember, be sure to have fun while drawing your favorite animal!