There are a total of 12 training manuals.
Shiv: Sharpening (increases shiv use) in the
Bill's Town bar hideout.
Health: Splinting (increases health restored) above the first
Pittsburgh garage.
Shiv: Reinforcement (increases shiv use) in the
Pittsburgh hotel lobby safe.
Melee: Knots (improves weapon upgrades) in the corridors after beating the
Pittsburgh hotel basement.
Molotov: Construction (increases molotov blast radius) in the
Pittsburgh apartment where you first meet
Henry and Sam.
Bomb: Containment (increases nail bomb blast radius) in the
Suburbs sewers just after finding the Shorty shotgun.
Melee: Techniques (improves weapon upgrades) in the
Suburbs brick house, in the attic.
Smoke: Chemistry (improves smoke bomb duration) at
Tommy's Dam, to the left of the workbench near the generators.
Health: Sterilization (increases health restored) at the University, in the building on the right of the
monkey-filled courtyard.
Molotov: Deployment (increases molotov blast radius) in the
University Science Building, behind the Shiv Door.
Smoke: Shaping (improves smoke bomb duration) when approaching
David's Lakeside Resort base as Joel, go through the motel to the shed Shiv Door and open it.
Bomb: Shrapnel (increases nail bomb blast radius) past the
Bus Depot and Triage, on top of the semi-truck near the tunnel Bloaters.
Source:
https://www.gamesradar.com/the-last-of-us-training-manuals-r...If you'd like a video guide for reference, check out PowerPyx on YouTube: