I have gotten some items that are of the type "follower". How do I equip those items? One example of this is called "the trinket". Nothing happens when I try to right click.
You don't equip them. Your followers do.
Each follower (Templar, Scoundrel, and Enchantress) has a special equipment slot just for these types of equipment. You can access these slots through the follower inventory screen.
The inventory screen can be accessed by clicking on the follower icon at the top left of your screen or hitting the 'F' key (by default) if you want to access the inventory of the follower you are currently using.
The inventory of followers you are not currently using can be accessed by dialog options with them in town.
You need to open your follower's inventory screen and equip it there.
Click on the portrait of your follower (if they are following you) or click on them in town (if not following) and open their inventory.
Once the inventory is open, you will be able to right click the item and it will equip to the follower's open slot.