There are a lot of different ways to go about adding texture. It really depends on what you need. As a start, I'd recommend trying to get a good handle on working with shading before worrying too much about texture. Texture without shading almost always looks awful.
I'm assuming you are mostly looking for fur texture, is that correct? The basic way to do that is with the brush and smudge tools. If you want something closer to a realistic fur (which may or may not look good on your drawing depending on the style of it.), you could try this:
-Select the area you where you want the fur.
-Add a little bit of Noise (Filter->Add Noise). Make sure the "Monochromatic" checkbox is checked.
-Use the Smudge tool to smear the colors in the directions you want the fur to flow.
I'll again stress that for this to really look good, the shading, drawing, and so for will need to be fairly good too or it just ends up looking like a bad photoshop effect.
