The Last of Us Part I

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: