1/8: The earliest slab obtained comes from Siegward's questline. First, you must talk to him in the Undead Settlement, and force his hand there. Then you'll eventually encounter him trapped in a well. Find and give him his armor, and he'll climb out offscreen. Later on in the game, Siegward will be encountered resting in front of a bonfire. Talk with him here, then proceed to the Irithyll Dungeon. Navigate through this area and acquire the key at the end of a sewer filled with basilisks. You can then use this key to open Siegward's cell, found hidden much later on in the same level, requiring a small bit of acrobatics into a window from a rooftop. Once he is free, you are able to receive his assistance during the Yhorm fight, which, upon defeat, will grant you your first titanite slab.
2/8: The next titanite slab can be obtained by defeating the Dancer of the Irithyll Valley, Oceiros, the Consumed King, and finally, Champion Gundyr, who will then drop a Coiled Sword Fragment, which you can drop inside the invisible NPC's nest on top of Firelink shrine, transforming it into a slab.
4/8: After defeating Oceiros, collect the gesture off of a knight's corpse in a proceeding room, and use it on the red carpet area nearby an elevator, found much earlier in the Irithyll Dungeon area, several locations prior. It will transport you to Archdragon peak. From here, defeat the Ancient Wyvern, unlocking the rest of the level, allowing access to a lone Titanite Slab near the very end of the level, and also allowing access to the Nameless King, one of the game's most challenging fights. Upon defeating him, the room you will appear in afterwards contains one more slab.
7/8: In the penultimate stage of the base game, Grand Archives, unlocked after defeating Dragonslayer Armor and 3 Lords of Cinder, there is a grand total of 3 titanite slabs. One is hidden behind a bookshelf, opened by a lever. One is hidden inside a double-elevator near the boss room.