Instruct the building supply company to cut your plywood sheet in half, leaving you two pieces of plywood that measure 4 by 4 feet and are 1/2 inch thick.
Measure across the top of the spool to get the spool width. Measure across the plywood square to find that width. Draw a cross on the plywood with one line going down the center of the board and one line going across the center. Subtract the spool width from the plywood width to find the overhang. Divide the overhang by 2. Measure down each of the lines from all four edges to the distance you figured and make a mark. When you lay the spool on the plywood to center it, all four dots should be right at the edge of the spool. Center the spool on top of the square.
Turn the spool right side up, keeping the plywood exactly in place. Screw the plywood square onto the wooden spool circle. Space the screws halfway between the center of the square and the edge, and place them at 2, 4, 6, 8, 10 and 12 o'clock. Tighten the screws until the flat heads are sunk into the wood.
Spread a generous amount of wood glue onto the surface of the plywood square. Center the other square on top of the first with the rough side down. Match up all four edges exactly.
Place cinder blocks or other heavy objects on top of the plywood to hold it down while the glue is drying. Allow the glue to dry for 8 hours to achieve a secure hold. Cover the table with a square tablecloth to finish.