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.
Many crayon artists (you can find a few online) use solvents to soften their appearance. It can be a wonderful look but, personally, I love the pixilated look the crayon creates when applied just as is. Look at the art examples in this post _ you can see the speckled look crayon has when applied in layers. This adds to the realism, especially when creating an out_of_focus background, such as in these two images.