The board works like any other xy table, with a few key differences. First, the x axis has an extra servo attached to it, which raises and lowers a magnet. The magnet is attracted to pieces on the chess board above, allowing them to move. Second, embedded in the board are 64 magnetically activated reed switches, allowing the arduino to know the location of each piece.
What I love about this project is its adaptability. If you decide you're done with it as a chess board, it can instantly convert into a CNC mill by modifying a few pieces. I'll talk more about this possibility at the end.
All in all, though I learned a lot from this project and had fun building it, the board was not as successful as I had hoped. The magnets were way too powerful, so extra pieces would almost always drawn in when they shouldn't have. However, with a few thoughtful changes I think this could have been a better, more functional project. Until I build another, better board, though, I think this Instructable still serves as a pretty good guide to make your own chess robot.