Peg Solitaire (also known as Hi-Q) has very simple rules. Pegs (red circles in this implementation) are allowed to jump over adjacent (vertically or horizontally) pegs. The peg that has been jumped over is removed. So jumps are like captures in Checkers. To move a peg, you select it first by clicking on it once. Then you click at the square (hole) to which you want the peg moved.
The goal of a regular game is to reverse a starting configuration: Positions with pegs must become empty while empty positions should be filled with pegs by the end of the game. At the beginning, you are presented with the standard configuration where just one peg - the central one - is missing. Therefore, the goal for this configuration is to end up with a single peg in the middle of the board.
Other starting configurations are available. In some, the goal is to reverse the starting configuration. In others, to end up with a single peg at the center of the board. (In the applet, there is a normally disabled checkbox Center to indicate the goal.) Configurations are selected from a combobox at the lower right corner of the applet. Do not be afraid to experiment during the play: you can always backtrack by pressing the Undo button. You are able to retract as many moves as you made in a single game.
You may try creating your own starting configuration by selecting "Design your own". The Set position button becomes enabled. When it's checked, you either set or remove pegs from the board. When unchecked, you play the game. If you discover a nice starting configuration, I'll be happy to incorporate it into the applet with due references.