Consistent Pressure Gives a Uniform Look. Keeping a consistent pressure with the crayon on the paper gives a uniform, pleasing look. If you're pressing hard, your hands will get tired quickly, so I prefer to press lightly. Interestingly, being aware of how much pressure you're applying seems to be really hard for younger children. It must be tied to motor skills in some way. It won't hurt anything to tell them this tip, but if they aren't implementing it, just let it go.
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.