Measure the internal width and length of your iron bed frame using your measuring tape.
Cut the plywood sheet to match the width and length of the frame. If you have a queen or king size frame, you'll need to use two plywood sheets. Cut each to match the width of the frame and 1/2 the length.
Sand one face of each plywood sheet. You can sand all faces, but only one face will come into contact with your mattress. Similarly, you can paint the sheet at this time -- but since no part of the plywood will be visible, it's not necessary.
Set the plywood into the iron bed frame, as if you were setting a mattress in place. If you had to use two sheets, place them side by side -- running perpendicular to the length of the mattress.