To move a piece simply move the mouse pointer over the square of the piece you wish move, click the left mouse button to select the piece. You can then hold the mouse button down and drag the piece to the destination square and let go to make the move.
When Guess move (Preferences->Board tab) is off you can select the source square with a click/release of the left mouse button and then select the destination square. However we believe most people will prefer to use the much faster Guess move approach which is on by default.
You can read about more advanced move entry capabilities in the Game Board section.
If you have guess move enabled you will notice as you move the mouse over a square of a piece you can move, the best expected destination square is highlighted. You can select that recommended move simply by clicking the mouse button and releasing it.
Alternatively with the mouse pointer over a piece, if you then click the right mouse button guess move will highlight what it thinks is the next best destination square for the piece highlighted. Repeatedly pressing the right mouse button will cycle through the moves in order of quality. Click and release the left mouse button to select the currently highlighted guess move.
Also if you move the mouse pointer over a square which a piece can move to you will see the best source square for that move highlighted. If you want to select that move simply click and release the left mouse button.