Miter cut the sides of all four 24-by-24 inches planks to 45 degrees so that the mitered sides will mate to form the corners of the box. If you don't have a miter saw, you can use a miter box with a handheld saw instead. A miter box is a simple cutting guide for making angled cuts.
Run a line of glue along the mitered sides. Form them into a box, then use the band clamp to hold the box together while the glue dries. Drying time is about 2 hours.
Drive a finishing nail every 4 inches through the side of the planter box into the glued joint while the band clamp is still on. After all the corners are secured with nails, remove the band clamp.
Lay the two 10-by-24 inch planks flat on the work surface around 2 inches apart and parallel to one another.
Place the four 5-by-24-inches planks across the two 10-by-24 inch planks, evenly spaced. There will be around an inch overhang on each end of the 5-by-24 inch planks. The two planks on the side should be flush with the ends of the 10-by-24 inch planks.
Nail the 5-by-24 inch planks down, using four nails into each 10-by-24 inch plank -- 8 nails altogether for each of the thinner planks. This is the base of the planter.
Place the base of the planter over the top of the box (which will soon be the bottom) with the 10-by-24 inch planks facing up. Nail the base to the box through the ends of the 5-by-24 inch planks.
Invert the box so that the base is now on the bottom. Lightly sand the planter box, then paint or varnish it. Paint with the grain of the wood.