The biggest key to painting animals, or any subject for that matter, is to really look at and observe the reference you are using. Look closely at the shapes, patterns, shadows, and highlights of each part of the animal before you begin to paint.

Quick tips for better painting animals:

• Make sure your brush strokes go in the direction the fur is growing to get the most realistic effect. 
• Pay attention to the texture of the fur and decide how you want to paint it. Do you want smooth washes for short-haired animals or long chunky brush strokes for long-haired animals? Practice on a scrap sheet of paper to decide on the technique that works best before starting your painting. 
• White has other colors in its shadows, like blues, grays, or beiges. Nothing is pure white.
• Pay special attention to the eyes, notice where the highlights are and if there are any reflections in the eyes. Humans are naturally drawn to the eyes of a creature. So be sure to paint the eyes with as much accuracy as possible. 
• While you may use black paint straight from the tube, it may look more realistic to mix your own dark color. For example, my favorite "black" is a mixture of burnt umber and indigo blue. There are many combinations you can mix to get a black, experiment, and find the best one for you. 

I hope these tips help! Happy Painting!