You'll need Aileen's Clear Gel Tacky Glue, and fur.
I use Viscose doll hair but only because it is the thinnest I can find and I need thin for micro mini's. You can use anything though.
Add the fur in very thin layers, and just a few strands at a time. Start from the back of the animal, (leg or tail) then work your way up to the snout. For areas with thin fur (snout, paws ect..)I create flocking by cutting the fiber into a nearly powder like consistency.
To add color Start by dyeing/finding fur which matches the lightest shade of the real animal, The rest of the color (highlights, shadow, markings) is added with inks or Acrylic paints.
A couple of years ago I created a tutorial for sculpting and furring a Yorkshire Terrier. It is complete instructions from lump of clay to finished, furred, painted Yorkie. It is available here: http://store.payloadz.com/detail_html.asp?i=944907