To implement the last test, we should store the location of the placed pieces in an array. Every time a new piece is placed, we should verify that the place is not occupied, or else throw an exception:

private Character[][] board = {
  {'', '', ''},
  {'', '', ''},
  {'', '', ''}
};

public void play(int x, int y) {
  if (x < 1 || x > 3) {
    throw new RuntimeException("X is outside board");
  } else if (y < 1 || y > 3) {
    throw new RuntimeException("Y is outside board");
  }
  if (board[x - 1][y - 1] != '') {
    throw new RuntimeException("Box is occupied");
  } else {
    board[x - 1][y - 1] = 'X';
  }
}

We're checking whether a place that was played is occupied and, if it is not, we're changing the array entry value from empty () to occupied (X). Keep in mind that we're still not storing who played (X or O).