Start by cutting off about 1-inch slices off of both ends of the watermelon. Try to cut as evenly as possible.
Stand the watermelon on one of the blunt ends and cut the watermelon in half length wise, top to bottom.
Cut the halves into halves so now you have 4 quarters.
Lay one of the quarters, rind side down on a cutting board. Using a sharp knife, carefully cut the watermelon slices to the thickness you desire.
Repeat with the remaining quarters.
Rindless cubes or sticks
Start off by cutting both ends of the watermelon off to make blunt ends, about an inch worth.
Stand the watermelon upright and using a long, sharp knife, carve down all the sides of the watermelon rind only cutting off the skin, about an inch deep. Repeat all the way around the watermelon until all that is left is the pink watermelon flesh.
Once all of the rind is carved off, cut the watermelon into half and then into quarters.
You can cut into smaller cubes or longer watermelon sticks at this point.
Video
Notes
If you don't plan on eating all the watermelon, only cube what you are going to eat and leave the larger pieces uncut so that they do not lose their juices as easily.