Measure the size of the queen size mattress. You should leave four to six inches between the upper bed and the trundle bed's mattress.
Cut the wood base, with a saw, in the size of the mattress. Leave 1/2 inch in length and width extra so there is room for error. Cut two more pieces of plywood in the same length and two of the same width as the first piece you cut.
Put all four pieces of board together. Nail the pieces of plywood together using L-brackets on the inside of the boards.
Nail the frame to the pieces you have put together with the L-brackets.
Flip the bed over and put wheels on each corner of the bottom of the trundle bed, using screws to keep the wheels in place. Use small enough wheels so that the trundle bed can fit under the main bed; make sure the wheels are the same size.
Paint the trundle bed to match the main bed. If you do not wish to paint it, you can stain it. After the bed dries, slide it under the main bed to make sure it fits. You can now start using your bed!