First things first, I use a drawing tablet (which gives me pressure sensitivity) and few self made fur brushes in Photoshop. They are much more convenient and much less time consuming than drawing each individual piece of hair.
Make several dots on a canvas and go to edit>>define brush and that will create your brush. Then make sure in the brushes tab Shape dynamics is checked and in Brush tip shapes change the spacing to 1% you now have nice fur brush. I recommend making several other brushes of different shapes as well, this will give your fur more variety and it won't all look alike.
1. At the moment I have my background on one layer and I'm drawing my fur another.
Using a brush I start off filling in the base fur colors. My personal brush preference is the Hard Round #19 brush set to wet edges. It makes for a nice watercolor look.
Start by making fast strokes in the direction of which the fur is flowing.
2. Continue on until the whole area is filled. You don't want to completely color everything because notice how the brush already begins to show clumping. Hair naturally clumps and it will make your fur look more realistic.
3. Now we are going to bring out those clumps and bring more of a shape to them by adding in some shadows with a semi darker color than your base color. This makes it appear like there's some separation in the fur and also helps us to know where to start drawing our detailed and individual pieces of fur.