I know this isn't the best and the image I usde is maybe two years old, but I still use this technique.
Not a great tutorial but I noticed that you can hardly find any colored pencil tutorials. I am just a total traditional art noob, so bare with me.

Materials I use: Prismacolor pencils, Polychromos, Micron Pen, some sketch paper (preferable smooth and thick), special pencil sharpener (it's actually one of those sharpeners you use for those eyeliner pencils, they are specially made for soft leads )

What you can use: Any kind of colored pencils, they don't have to be expensive, but be sure to use some with a soft lead and bright colors. Also some with a harder lead for more defined strokes are good. Mix them. Any kind of fineliner, preferable black. Use different tip sizes.

Ok, on with the method.
With this technique I work from dark to light. I usually use between three and five colors to achieve the desired effect. Normally I use black as the darkest color. Than I used in this example three different shades of green, and yellow for the highlights.

1. With grey I outlined clumps of fur.

2. With black I drew in the darkest shadows.

3. Now I took the darkest green to refine the shadows.

4. Second darkest green, more refining.

5. Lightest shade of green and already a bit of the yellow, and more refining.

6. At the end I took the yellow and made the hightlights stronger and also blend the other colors together with it.

So, and if you don't wanna draw such a dark fur color you can use different shades of grey instead of black for the first shadow, like I did on the orange part of her arm.