JustBats.com provides a good sizing chart for youth baseball bats, as of 2015. To use the chart, one must know the child's height and weight.
Youth bats range in length from 26 to 34 inches and a drop between minus 10 and minus 13.5. A bat's drop is its length to weight ratio. A bat that is long and light swings fast, but with little inertia. A bat that is short and heavy swings more slowly, but has greater inertia. Select a bat by first getting a correct length using the sizing chart. Find the proper drop by trying several bats in the correct length and selecting the one that is easiest for the player to control.