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.
Stay sharp! Good quality pencils will allow the lead to be sharpened regularly. Needle sharp tips on your pencils are perfect for applying detail and getting the precision required to color intricate areas of a design. Thinner points will give you more control over the color produced, big fat rounded ends on your pencils make it difficult to get the brightest colors.