Set out two 3/4-by-24-by-36-inch plywood boards on the working surface, parallel to each other. Get help from an assistant to have the two boards, which are the sides of the kids' entertainment center, stand up on their long, thin sides about 2 feet apart from one another. Set another plywood board with measurements of 3/4-by-24-by-24 inches against one pair of the side board ends.
Position 1-inch metal L-brackets every 6 inches on the inside of the frame at the joint between the side boards and the new board, which is the top board of the entertainment center. Screw these brackets into place by tightening 3/4-inch wood screws into each of the metal bracket attachment holes. Repeat with another 3/4-by-24-by-24-inch board at the other end of the side boards to add the bottom board.
Set a 3/4-by-24-by-37 1/2-inch plywood board on the working surface and lower the frame on top of it so the frame is even with the edges of this larger plywood board, which is the rear board of the entertainment center. Position 1-inch metal L-brackets every 6 inches around the inside of the frame where the rear board meets the frame. Attach the brackets to the frame and the rear board by screwing 3/4-inch wood screws into the holes.
Stand the entertainment center upright and position a 3/4-by-22 1/2-by-24-inch plywood shelf board at a desired shelf height. Set two 1-inch L-brackets underneath the shelf against each side board. Attach each bracket in place with 3/4-inch wood screws. Repeat to install as many shelves as needed.