See the Wikipedia article of the original game for a thorough description.
The computer makes a code of colored pegs. Your goal is to figure it out based on the feedback given by the computer.
You get feedback in the form of white and black key pegs. A white key peg means that one of your pegs is of the right color, but in the wrong place. A black key peg means that one of your pegs is both of the right color, and in the right place.
Start a new game by clicking the "Start new game" button on the left.
Select a peg color by clicking a peg in the bottom row. The currently selected color is highlighted.
Place pegs of the selected color by clicking the fields of the active row on the game board.
Press the "Guess" button to make the computer evaluate your guess.