You are Link, the computer is Rauru. Select a piece on your side (the top side) and click a square diagonal to it to move your piece. Normal Checker rules apply. First to jump all of the opponent's markers wins.
Once you get your marker to the opponent's back row, it will change to a King. A King is signified by a little K in the lower left-hand corner of the marker. It's hard to see, but you can tell the diffrence.