Obtain reference pictures of the animal you want to recreate. The more pictures you have, the easier your job will be. Information on physical proportions is also useful.
Glue together sheets of foam until you have a block large enough to carve the animal out of.
Sculpt the animal. It's best to use saws and knives to first cut out the basic shape, the go in with carving tools to refine the form and add detail. Exaggerate any details. You will lose finer details in the fiberglassing process, so don't waste your time with them.
Cut or tear the fiberglass into manageable squares.
Mix the fiberglass resin and catalyst in a paper bucket with a paint brush.
Brush a layer of catalyzed resin onto the form.
Overlap squares of fiberglass onto the form, pressing them into the resin.
Tap more resin into the fiberglass with the paintbrush, saturating it fully. Tapping the resin instead of brushing it helps to eliminate trapped air bubbles.
Add another three layers of fiberglass and resin (four to five if the animal will have children sitting on it).
Allow the fiberglass to fully cure until it is no longer sticky to the touch.
Sand the fiberglass smooth, starting with coarse sandpaper and gradually moving to finer and finer grits. You can also use an electric sander to speed up the process.
Paint the animal. This can be done with spray, automotive or acrylic paints.
Spray several thin coats of acrylic enamel spray to seal the paint and add a glossy shine.