There are two ways to access The Ringed City.
If you have already completed Ashes of Ariandel, a second bonfire will appear in the final boss room, near the statue of a snake. Simply interact with the bonfire, and you will be transported into the first level of The Ringed City DLC.
Check out our Ashes of Ariandel walkthrough if you need help completing it in preparation for The Ringed City.
If you have not completed or do not own Ashes of Ariandel, you can still access The Ringed City, but you will need to have access to the final boss fight first.
Travel to the bonfire outside the final boss fight of Dark Souls 3, then turn around. A second bonfire will be there behind you. Interact with the new bonfire to be teleported to the first level of The Ringed City DLC.