Use good quality crayons (Crayola works well) for the best results. Making the fill color darker around the edges is a good technique for adding dimension. As you work, don't press too hard. It's better to add layers of color than to have too much color that you can't remove. Take care to color evenly and without causing color streaks. When you're finished, place a piece of scrap fabric over the coloring and iron the paper on a high setting. This will heat set the coloring and remove excess wax.
Quality Matters. Not all colored pencils are the same. Cheap colored pencils tend to have harder wax leads and less pigment which mean they produce less vibrant colors and have a tendency to leave some white spaces uncovered in the grain of the paper. Because the lead is hard, cheaper pencil leads often have a tendency break and if the lead breaks throughout the length of the pencil you can be left with something that is unusable.