You are in a field that has been divided into squares. Mines have been planted under 99 of those squares. Your task is to clear all of the squares which do not have mines, leaving the 99 mined squares.
Left-clicking on a square clears it. If you clear a square that actually is mined, the mine explodes and the game is over. If the square is not mined, the number that appears in the square is the number of adjacent (horizontally, vertically and diagonally) squares that are mined. When you start the game a small area of the board is automatically cleared so that you do not have to begin the game guessing blindly.
Right-clicking (shift, click on a Mac or other computer that does not have a right-click concept) on a square marks it with a flag to denote that you think the square is mined. The counter in the upper left corner is the number of mines left to discover, assuming that all your flags have been planted in squares that actually are mined.