Once you have the configuration you want, begin securing the pieces together. To do this, start with two sides of the first hexagon. Run a bead of wood glue where the two cut angles meet. Fold the angles together and press firmly, allowing the glue to seep out and wiping up as needed. Place a piece of painters tape along the corner to act as a clamp as the glue dries.
When the glue has begun to set, use a nail gun to run two 1-1/4-inch brad nails through the angled side of the joint and into the straight run of the other board. You can alternate the sides of the joint you nail, if desired. Repeat this process with the remaining pieces to complete your first hexagon. Repeat this process to connect your remaining hexagons. As you secure pieces to already formed joints, you may need to do one nail in the center instead of two nails on either side.