If you have a little helper in the kitchen, you may be thinking about getting him or her an apron of their very own. One of the benefits to making it yourself is that you can choose a fabric that will really hit it big with your little boy or girl. The Michael Miller blog has an excellent post for creating a child's chef hat and apron, which was the basis for the children's apron sets that I sell at my Etsy shop.
I made one important modification to my aprons, which I think makes them much more usable, especially for a child. Instead of having separate ties at the neck and waist, my apron is tied using a single tie that runs through channels connecting the waist and neck. This allows the apron to still fully adjustable at the neck and waist, but you only need to tie one bow. And the ties are extra long (I make mine 100 inches), so it can be tied in front which I think is easier for someone trying to learn how to tie a bow!
The channels are made using single-fold bias tape. You attach the bias tape to each arm hole as you normally would if you were binding the raw edges. When you fold the tape to the inside, make a channel for the ties to slide through by sewing at both edges of the tape. For the tie, just fold the single-fold tape in half to make a double-fold tape that fits perfectly in your channels.