Lay your plywood flat and set each board on top of the plywood so the ends and edges are flush. Observe the grain pattern on the boards. Arrange them according to your liking. This is called dry-fitting your boards.
Glue the boards to the plywood. Use two wide beads of glue for each board. Push the edges of the board against each other so there are no gaps. Let the glue dry according the instructions found on the bottle.
Scrape away any excess glue from the top or edges hardwood chair mat. Scrap in a motion that is parallel with the grain.
Sand the entire chair mat using your medium-grade and then fine-grade sand paper. Sand in a motion that is parallel with the grain of the wood. Apply your wood stain evenly over the boards and let the stain dry according to instructions.