In a manner similar to the traditional game of GO, when you surround any space with three stones (they don't have to be occupied), that space will be captured on your next turn and a stone will be placed on it.
Fill more than 1/2 the board to win.
You get two moves per turn. Optimally place one stone from your bowl and move 1 stone on the board (though technically you could move two stones on the board and elect not to play from your bowl. Note that when you move a stone on the board the space it once occupied is still owned but vulnerable to attack.
You may attack/capture any unoccupied space, even if it belongs to your opponent.