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Look at the color wheel to help determine which colors you should use. Colors across from each other on the wheel will be very distinct, while colors in close proximity will look good next to each other. Choose a set of colors that give your sprite a distinctive look without being too jarring. Avoid pastel colors if possible, unless the entire project uses that style. The more color you add, the more distracting your sprite will look. Take a look at some of the most iconic sprites and you'll find that they often only use a few colors.  Mario - The classic Mario sprite uses only three colors that are all closely related. Sonic - Sonic has more detail than the original Mario, but is still only composed of four colors with varying shades. Ryu - One of the classic fighting game sprites, Ryu uses large areas of simple colors, with slight shading for definition. Ryu has five basic colors with various shades. Use the Fill tool to apply your color choices to your sprite. You're just applying base color at this point, so don't worry about how flat it looks. The Fill tool will replace all the pixels that match the pixel you clicked with your selected color, until boundaries are reached.
Brush up on basic color theory. Just use a few colors. Apply your colors.