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.
Concentrate on the basics. If you are just starting to color, keep things simple. Forget shading, burnishing, details and texture _ start off by block coloring and concentrating on keeping between the lines. Block coloring is simply the practice of taking your colored pencil and filling an area completely and evenly with that color. Get to know your pencil, feel the weight of it and practice control. Simply filling those spaces with color whilst trying not to go beyond the lines will help you master control and prime you for learning more advanced techniques.