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.
Overlap Colors to Create a Blended Look. I like to lightly color the dominate color first and leave a bit of paper exposed for the wax of the second color to cling to. In the liver I colored (below), I started by coloring a layer of red, then I colored some brown on top. Then I colored more red over the top. I find this kind of layering to be really fun!