If you repeat the same move three times, the game will automatically end in a draw. Just keep track of your moves and try not to repeat the same move three times. Even if your opponent repeats the same moves, as long as you change your moves, the game will not automatically end in a draw.
There is one error, though. I'm not sure if they've fixed it yet, but the game will automatically declare a draw when each player has only one piece left. So even if you have a winning position, if both players end up with just one piece, the game will still be declared a draw.