If you are unable to equip it, check its details to ensure that it can be used by that particular hero. Finally, open the trinket menu with triangle (Ps4), Y (Xbox One) or X (Switch), and put the trinket into the open slot on the hero. Hold R2 (PS4), RT (Xbox One), ZR (Switch) to scroll through your roster, then bring up the character’s stats/skills page with square (PS4), X (Xbox One) or Y (Switch). You can equip a trinket while in the hamlet by first selecting the desired hero. When a hero dies in Darkest Dungeon, any trinkets they were carrying will be lost at first, but retrieved as part of your loot upon exiting the dungeon. Each will have different attributes, and some can only be equipped by certain classes.
Trinkets can be found while on an expedition and as a reward for various quests, or purchased from the Nomad Wagon for a pretty penny in Darkest Dungeon. Though you may breeze through your early expeditions without ever even trying out any trinkets, the most dastardly foes down in the Darkest Dungeon will practically demand their use, if you hope to survive with all limbs intact.