Lay a vapor barrier down over the concrete. Roll out the vapor barrier onto the concrete and cut it to fit. Attach it to the concrete with adhesive.
Score the back of the sheets of plywood with a scoring tool to a depth of a half inch. This will help provide a better grip for the adhesive.
Cut the plywood to fit with a circular saw. Use a combination of 2-by-4 foot lengths and 4-by-8 foot lengths to fit the room.
Coat the back of the first panel with construction-grade adhesive. Use a gun delivery system to spread the adhesive evenly.
Press the first panel onto the concrete. Stamp it down to create a firm bond with the floor.
Repeat with the remaining sheets. Do not line the rows up. Vary the installation by starting with one larger sheet for one row, and then one smaller sheet for the next row. Continue until all the plywood is down.
Let the adhesive cure according to manufacturer directions. Do not allow foot traffic on the floor until this time period has elapsed.