To start off, you need to have your PSD file that has your line work in it opened in Photoshop. You also need your Layers box open. If your Layers box is not open, you can open it by going to Window>Layers. For the moment, the only layers are the Lines and Background layers so we're going to have to add a few more.
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In the Layers window, click the "New Layer" button (as shown in the example below). A new layer will appear above the selected layer. We're probably going to need a total of three new layers for this piece, so click the button three times.
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Now, since the lines are going to be what overlay all of the coloring, we want to move this layer to the top of the stack. Click and drag the Lines layer to the very top of the stack like so.
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All of these new layers could use some names. These are going to be color layers. Double-click on the name of each listed in the Layers box to rename them to Color 1, Color 2, and Color 3.
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The document is now set up and ready to go! Time to add some color!
Choose the Magic Wand tool from the Tools window and pick a place that you want to fill with your first color. I usually start with the main body/fur color. Make sure you are on the Lines layer. Click inside the area you want to select and watch how it selects everything inside the lines like magic!
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If it selects more than you wanted, that means you have a gap in the lines somewhere. You'll have to zoom in and fix the gap using the paintbrush tool.
Now, this selection should be a little tiny bit wider so it overlaps the edges of the lines a bit. Go to Select>Modify>Expand. Enter a value of 1 or 2 depending on the size of your image. If they don't overlap enough or go outside the lines you can undo and try it again with a different value. Usually one or two work fine but if it's a really large, high-res image you may need to pick a higher number.
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Now go down to your first color layer, Color 1. Choose a color you want this selection to be filled with. Go to Edit>Fill. Use the default fill options.
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You will now see that the selection has been filled with this color.
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Go through the rest of your image and select areas of the same color to fill.
The idea behind using multiple color layers is that you will be able to shade in and adjust color very easily, without bleeding into other areas.
You can organize your color fills however you like. I prefer to keep single objects, planes, or parts on the same layer (such as all of this dog's base fur color). You can have multiple areas of color on a single layer, but try to avoid having any touching areas on the same layer (I could have the eyebrows and the tongue colors on the same layer, but not the tongue and the base fur color). I know all of this seems a bit confusing right now. Just hang in there, it will hopefully make more sense as we go along.
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Now I'm moving on to the Color 2 layer. I decided to fill in the tongue, eyebrows, inner ears, eye whites, and bottom of the nose on this layer. Notice how none of these areas are touching.
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I repeated this process for each selection, organizing them into different layers (in this case, all I had left was the top of the nose and the irises on layer 3), until I had all the basic colors blocked in. Don't worry about details like lighter markings or other things with soft edges. We'll add those in a little while. Right now we just want to get all of the solid colors that are contained by lines blocked in.
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For those of you who were a bit confused by the layer organization trick, I will now try to explain it more clearly. I've taken some screen shots to show you how I've organized the colors in this image. Color 1 contains only the main fur color for the body and face. Notice how it is all one single color.
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Color two contains the bottom of the nose, the whites of the eyes, the eyebrows, and the tongue. Notice how none of the different colors are in areas that are touching each other? This will make your life much easier when you move on to shade this thing or add markings and other adjustments.
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Color 3 contains the the irises of the eye and the top of the nose. Once again, notice that no two different color areas are touching each other
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Here's one more diagram to help illustrate how this works. This color chart should help illustrate the organization method a bit more clearly. You can easily see here how none of the separate areas of color that are on the same layer are touching each other
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Now, hopefully that makes more sense (if you're really still confused, just try your best or jump ahead to the Painter tutorial and you'll see why we did this).