Facing the throne in front of the Abundance Fountain, keep following the left path until you reach an intersection: take the narrowest path (the left one) and look up. Do you see the Regaleira Tower up there? If you do, you're going the right way. Pass under the stone bridge and keep going. The grotto is located right beside the first tower you just passed.
As seen on
Quinta da Regaleira: The Highlights