Clavicus Vile's Shrine is a Daedric shrine southwest of the Imperial City. It is just east of the Ayleid ruin Ceyatatar, on the opposite side of the Gold Road.
Anedhel, Gul gro-Burbog, and Ma'Raska can be found worshipping here. Ma'Raska begins the related quest, Clavicus Vile, once you reach level 20; to proceed, an offering of 500 gold must be made to the shrine. During the quest, the giant dog statue will vanish, appearing instead in your inventory as a statuette.
Two benches are in front of the shrine, with two lit candles on a rock nearby.