There are twenty-five green squares, and these squares each contain either a Voltorb (equivalent to zero) or the numbers 1, 2 or 3. When you tap a square, you will flip it over to see what it contains.
At any point in the game, your score is equal to all the numbers you've flipped over multiplied together. This inevitably means that once you flip over a zero, you've lost all your points and can never get them back. But just to make the imagery a bit stronger, the zeroes are Voltorb that will violently explode and end your game immediately (after all, there's no point in continuing when your score has a multiplier of zero in it). So you don't want to flip over the Voltorb. Likewise, the ones don't really matter; multiplying your score by one just keeps it the same. Therefore, the goal of the game is to flip over all the twos and threes on the table, and once you've done that, no matter how many ones are left, you'll get your payout and advance to the next level. If you flip over a Voltorb at any point, however, you'll lose all your winnings for this round, and if the number of squares you flipped before this happened is less than the level you're currently on, you'll drop back to the level corresponding to the number of flipped squares (though of course, since there is no level zero, if the first thing you flip over is a Voltorb you'll be sent to level one instead).
The top number in each of the squares is the sum of all the numbers in that row or column, while the bottom number is the number of Voltorb in that row or column. And from this, you need to work it out. You've got a memo pad to assist you, which allows you to give any square markers corresponding to Voltorb, one, two or three.
So basically Voltorb flip is a pokemon version of minesweeper.