Use the measuring tape to measure the height of your mattress and the depth of your waterbed frame. If your mattress is taller than the frame is deep, then you should be able to simply put the mattress in and enjoy. If the mattress is shorter than the depth of the frame, you'll need to insert the platform.
Subtract the height of your mattress from the depth of your frame.
Cut all four wooden strips to a thickness equal to the difference between mattress and frame. Cut the length of two strips to match the width of your mattress. Cut the other two to match the length, minus two inches.
Apply a coat of wood glue to one wide face of each wooden strip. Place them in the corners of the water bed frame, resting on the 1-inch thick faces.. Allow to dry.
Set the plywood sheet in place, creating a "false bottom" by resting on the edges of the wood strips.
Set your mattress in place. It should protrude half an inch above the top of the retaining planks.