First thing's first. Before you can start applying color, you need to get your canvas ready. Start by duplicating your linework layer. To do this right-click on it and choose "Duplicate layer...".

This layer will act to keep your lines intact even when you paint over them on the other lines layer. You should set the newer one created on top's blending mode to "Multiply" from the drop down box. This will cause only the dark lines to be visible, so the white areas will basically be invisible. Now this layer can truly function as only a "lines" layer. (Note that this isn't necessary if you inked on the computer)

Removing the white areas (aka negative space)
This step is only for those who inked on paper. Select the first lines layer that should still be on the bottom. Now we're going to use the "Magic wand". In its menu you want the tolerance to be around 30-40. Also, make sure "Contiguous" is unselected.

Contiguous basically means areas touching one another. So if you have two white squares and contiguous is selected, when you click on one white square, only that white square is selected as they don't touch. Now if contiguous is unselected you can click on either square and the other will become selected as well.

Now simply click in any of the white area, and with everythign selected, press "delete" on the keyboard. All the white area should dissapear.

With all the preparations done, it's time to add color. You're going to be working on the lower lines layer. This layer shall now be your "color" layer.

You will now use your paintbucket tool to click in each area and fill it with color. (You want about 10-20 tolerance.)

You may have to click in one spot a couple times to get it to fill out as much as you want.

Next you need to fill in the areas you can't get with the paint bucket. Use the brush tool to paint in the missing color and fill out all the lines.

Pure painting
Alternatively to using the filling method, you can simply use the brush tool to paint all the colors in by hand. To some this may be easier. It's a preference. Though, this is really the only way to do it if you went for the stylistic method and didn't ink your lines. It's just not clean enough to effieciently fill with the paint bucket.

An alternative style to coloring pretty much encompasses most of the styles at once it digital painting. Basically you'd be painting in transparencies and applying tones and colors in shades rather than each layer blending on one another.

Through this method you actually will be shading as you color. Often you'll be painting all on one layer. A great example of this method is a friend of mine's work over at Gone with the Blastwave. He has a couple good tutorials up here and here which will be a lot better in this area than I could explain.