How do I use the promotion items (and can I promote a Paladin to Pegasus Knight/Gladiator to Baron/Vicar to Mastermonk/Sniper to Brass Gunner/Wizard to Sorcerer)?
When your characters reach level 20, they can be promoted. Certain characters can have an item used in their promotion, to promote them to a special fighting class. The item must be in the inventory of one of your characters, it doesn't matter which - as long as the item is not in the caravan's depot. When you go to the priest and request a promotion, he'll ask whether you'd like to use the item in the promotion.
Note that characters who have already been promoted cannot be promoted again, eg if Chester has already been promoted to Paladin, he cannot then be promoted to Pegasus Knight using the Pegasus Wing (and no, even if he's a level 20 Paladin, it won't work). Characters can only be promoted once. Also, promotion items can only be used once, so (for example) you can't promote both Jaha and Randolf to Baron class.
Here are the promotion items, and who they can be used for (full details about the items and their locations can be found on the promotion items page).
Warrior Pride: Promotes Jaha or Randolf to Baron (BRN)
Silver Tank: Promotes Elric or Janet to Brass Gunner (BRGN)
Secret Book: Promotes Kazin or Tyrin to Sorcerer (SORC)
Vigor Ball: Promotes Sarah or Karna to Master Monk (MMNK)
Pegasus Wing: Promotes Chester, Rick or Eric to Pegasus Knight (PGNT)