You'll pick up this quest in Chapter 14 after hearing Kyrie's speech in the Sector 5 Slums. Head towards the Leaf House in the Sector 5 Slums and you'll spot a doctor standing outside the community center.
He'll hand over Doctor's List and task you with tracking down three items for him. This whole Quest relies on completing other Quests, namely the Subterranean Menace Quest so it's best to leave this one towards the end of the available Quests in Chapter 14.
This one is the easiest to find and you can get it as soon as you accept the quest. Return to Moggie to browse the Moogle Emporium and purchase the Moogle's Mortar for 1 Moogle Medal. If for some reason you don't have one on you, consider playing Whack-a-Box nearby, you'll get one just for participating.
This is by far the most difficult item to obtain on the list and you'll need to complete the Subterranean Menace Quest to do so, the Behemoth Horn will drop once you defeat the Type-0 Behemoth in the Underground Lab.
The final item is another straightforward one, as you head to the Church in the Sector 5 Slums as part of the Tomboy Bandit Quest, you'll find the item laying on the floor just in front of where Kyrie is standing.
Once you have procured all three items, return to the Doctor and hand them over to complete the Quest and obtain Telluric Scriptures Vol. III which grant 10 SP to Aerith.