Always Color in a Consistent Direction. This is my first tip. It will make a bigger impact on the end result than anything else and any age can use it! The changes in direction, shown on the red kidney below, on the left side, are what make it look sloppy, even though I carefully stayed in the lines. Coloring in a consistent direction, as seen on the other kidney, is easier on the eyes and ends up looking very tidy!
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.