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.
Whilst most colored pencils are wax based, some brands use an oil based lead, like Faber Castell's Polychromos. These pencils are very soft to apply color so will cover every fibre of the paper with their bright hues, but they are also very expensive and should only be considered if you are looking to take your art to the highest level.