For easy projects to start, try buying some wood cutouts on etsy or at the craft store, then you'll just need a sharp pocket knife, and you can shape the edges. Then sand it and polish it with something natural.
If you want to get into making your own cutouts, you can get a hand saw or a scroll saw, find the image of the animal you'd like to make, trace it on to the wood, cut it out, then continue with the whittling.
With your carving knives, always be sure to cut away from yourself, and buy a sharpener to maintain your knife and always keep it sharp, and of course, store it away from kids.