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To castle, move your king two spaces to the right or left. You can do this by either clicking on the king and then selecting the desired square (not the rook), or by dragging the king on top of the rook you want to castle with.
By default, you can click or drag pieces, but if you prefer to use only one method, you can customize this in your 'Board and Pieces' settings. Simply select your preferred option from the 'Move Method' dropdown menu:
Clicking on the king and then the rook will not castle under the default setting. This method, known as 'Legacy castling,' is not the default way to castle.
Legacy castling
You can enable Legacy castling—clicking on the king and then the rook—by going to your 'Board and Pieces' settings and selecting 'Legacy' in the dropdown for 'Castling method:'