I think the biggest problem people have when drawing with crayons is that they regress to being five years old again. They hold the crayon like they're coloring again, instead of applying it like a fine art medium. Another problem is that many people want to make it perform like colored pencils. While similar in application, they are quite different. You should not use crayons and expect them to behave like colored pencils. You'll be setting yourself up for disappointment.
Brighter results! Applying less pressure to the pencil will produce a lighter color, so how do you get that darker hue of the color on the page without pushing too hard? The answer is layers. Once you have mastered coloring between the lines with a nice even shade, you can take the same pencil and go back over that coloring again to provide a second or even third layer of color. Applying extra layers of color will remove some of the white grain that was missed in the first layer and bring depth to your color. Mix up the direction you color each layer to produce a smoother finish.