Poplar or birch woods make good choices to build a platform bed frame. These readily available woods look good stained or painted, and they come in a variety of widths and lengths. Full-size mattresses measure 54 inches long by 75 inches wide; if you choose, make your platform larger to account for overhang or to make space for a built-in bedside table.
If you build a full-size platform bed with a 4-inch rim around the perimeter, start with two hardwood boards measuring 75 inches long for the sides of your homemade bed, as well as five hardwood boards measuring 58 inches long for the top and bottom frame and the center supports of your bed. Use boards measuring 2 inches thick and 8 inches wide. The side boards will butt against the top and bottom frame boards, gaining the extra 4 inches from the thickness of those two boards. Complete the platform bed with a sheet of plywood to fit over the top of your box frame. Use metal L brackets to build the frame and connect the support beams, and wood screws to attach the plywood to the frame.
Begin assembling your homemade full-size bed by making a box frame with your hardwood boards. Attach two of the 58-inch boards with screws to either end of one of the 75-inch boards. Place the L bracket in the center of the boards and connect them so that the 75-inch side board fits flush against the 58-inch boards, with all of the boards flush at the top. Drill pilot holes before you try to insert the screws for the L brackets.
Before you attach your other side board, attach the three center supports. Place one in the center of the 75-inch side board and the other two halfway between the top and the bottom boards. Install the center supports flush with the top of the outside of your bed frame so the 8-inch width faces upward. Complete your bed frame by attaching the remaining side to the top, bottom and center supports.
Finally, attach the plywood sheet to the top of the frame to complete your full-size platform bed. Attach the plywood with wood screws placed every 2 inches around the perimeter and along the center support beams. Countersink the wood screws so the heads will not catch on the mattress.