Hey, remember how much of a pain it was to access the DLC area of the original Dark Souls? Well, From Software has mellowed over the years, and getting to Dark Souls 3's The Ringed City DLC is actually pretty easy. You'll need to have finished the previous expansion, Ashes of Ariandel, but otherwise accessing the bonfires that'll take you to the new area is very simple.
In fact, there are two bonfires you can use to access it. One is a new bonfire behind where the player spawns in the Kiln of the First Flame (ie, the final boss arena in vanilla Dark Souls 3), pictured below:
The second is found where the Sister Friede battle takes place in the Ashes of Ariandel area. Again, this is right behind where the player spawns at the Sister Friede bonfire:
If you're not seeing the bonfires in either of these places, chances are you've either a) not purchased the content b) not updated your game files or c) not completed Ashes of Ariandel.
While getting to The Ringed City's new areas is easy, completing it will not be. I hope you like being shot at from above!