The disc placed with the last move and the discs it flips cannot be flipped back, which is an advantage. The same holds inside a region: whoever enters an even region first gives away that region's last move if the opponent answers in the same region. Empty squares that touch only diagonally count as separate regions.
So White plays so that after the move, every region is even. Black must then enter an even region first, and White answers right away in the region Black entered, taking the last move of each region. From Black's side, the basic rule is to play odd regions first and enter even regions as late as possible (the parity rule).
Exercise
White to move. Find the move that enters the odd region so that every region is even afterwards.
Exercise
White to move. Find the move that enters the odd region so that every region is even afterwards.
Exercise
White to move. Find the move that enters the odd region so that every region is even afterwards.
Exercise
White to move. Find the move that enters the odd region so that every region is even afterwards.
Exercise
White to move. Find the move that enters the odd region so that every region is even afterwards.