Instructions
Ensure that you can legally castle. It is legal to castle when the king and the rook that are castling have not moved from their original positions, there are no pieces standing in between the king and the rook, your king is not presently in check and the king will not cross over or land on a square that is under attack by an enemy piece.
Hover the cursor over your king. Click and hold the left mouse button.
Move your king two squares to the left or right, depending on where you want him to castle (and where it is legal to castle). Release the left mouse button. Your king will move into the castling position, and the rook will be moved automatically into its new position.