After both sides were smooth I used paint masking tape in a square of 11 x 11 inches (Happened to be the biggest board I could fit on the slab I cut) and then put masking tape in rows of 1 3/8 inches horizontally and vertically. With 3/4 of the board masked off I used a dark stain from Menards, and you can see the result of that in the 1st picture. I had to take care with the stain, because unlike paint, the stain will tend to bleed into the wood, so I had to be extremely touchy with how much stain I used at the edges.
After that I masked the other portion of the board so I could finish staining the remaining black squares, as well as painting a 1/8 inch black edge around the border of the squares.
Once the painting was complete I finished the board with 6 coats of a semigloss polyurethane, sanding with 300 grit sandpaper between each layer to ensure a smooth finish. Additionally to finish the bottom, I used some felt furniture sliders to keep the wood from scratching the table.
I'm hoping to fit in a project to make some scrollsaw cut Chess pieces for the set, but for now It is making use of some checkers pieces we made from a 1 inch diameter dowel rod