Take one of the quarters and make cuts from the top part of the melon all the way down to the rind.
Make 1 inch slices from one side of the melon to the other side.
Take your knife and slice 1 inch strips down the length of the melon. (You are essentially making a crosshatch pattern on each quarter of the watermelon.)
After the cuts are made, start from one edge of the melon and cut along the rind.