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.
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.