1) Jewelled Mask
Availability: chapter 1
The exact location: You need to reach the main room of the jeweler's [Serendi Jewellers - Shop], i.e. the one patrolled by a single guard. Keep avoiding him, or distract him, and break into one of the shop windows next to the main entrance, which will allow Garrett obtain the mask.
2) Cornelius' Ring
Availability: chapter 2
The exact location: The Ring is in the office, in one of the last locations of the foundry [Old Foundry - Supervisor's Office] and you first need to break into the safe, which requires you to solve a pretty easy puzzle, first.
3) Ritual Book
Availability: chapter 3
The exact location: The Book is in the Underground Ruins, in the location with towers [Underground Ruins - Library Towers]. To steal it, Garrett needs to walk through the successive towers and solve a puzzle, at the very end.
4) The Talking Skull
Availability: The Happy Medium side-mission
The exact location: The Skull is in a locked chest at the warehouse's first floor [South Quarter / Riverside - Eelbiters Warehouse], where you should first distract the guard patrolling the area, before you collect it.
5) The Octopuss
Availability: The Carnal Connoisseur side mission
The exact location: The artifact is in the collector's vault [South Quarter / Riverside - Collector's Vault] that you visit towards the end of the mission, in the cabinet to the right of the vault's entrance.
6) The Mechanical Hand
Availability: The Hand Tailored side-mission)
The exact location: You will find the Mechanical Hand at the workshop [Stonemarket - Alfonso's Workshop] in the basement of the tailor's place. There is a single guard patrolling the place and you need to distract him, so you can break quickly into the safe with the collectible inside.
7) The Voice Box
Availability: The Silence is Golden side-mission
The exact location: You will find the Voice Box in the vault, at the ground floor of Oxheart Perry's [South Quarter / Riverside - Oxheart Perry's Vault]. After you locate the vault, you need to disarm the trap and use the lockpicks to open the safe.
8) Automaton's Heart
Availability: The Heartbroken side-mission
The exact location: Automaton's Heart is in the undergrounds of the Clockwise's building [Stonemarket - Project Pendulum] and to get to this artifact, you need to solve several logic puzzles.