D.M.
To make a checker/chess board use an exacto knife and a ruler to make even lines in the wood you want to use. If you want to get realy fancy, sand down an old end table/night stand for it. With the lines cut in you can easily stain just in the squares with a cloth so you have different colors. Of course comming up with checker pieces will be easy but you may want to check thrift stores for chess sets.
Balsa(sp?) wood is a great crafting wood for such things too. You can find it at hobby shops inexpensivly.
We've also made this same game with a bandana for a portible version. Just use a sharpie for your squares.
And ofcourse kids love to make up games! Have him help you create!