WoW Forever has transmog, and it's opt-in. You collect appearances as you play and can change how your gear looks at a transmogrifier in certain cities, or leave the system off. The rules below are from Blizzard's panel recap unless marked.
How appearances unlock
| Item | When you get the appearance |
|---|---|
| Poor (grey) and Common (white) | When you loot it, without binding it |
| Uncommon and Rare dungeon drops that bind on pickup | For every player in the group who could have looted it |
| Epic raid drops | Only for the player who gets the item |
You can only use appearances of the same armor type, so plate goes on plate and cloth on cloth. High-level appearances can only be worn at level 60. Blizzard says cosmetic-only exceptions will be rare.
Reported: an item that binds when equipped has to be bound or sold to a vendor before it counts, and the collection is account-wide (Shift+P), per Warcraft Tavern's transmog guide.
Classic or Enhanced preset
Transmog starts off on the Classic preset and on on the Enhanced preset (Blizzard's starter guide). With it off you still collect appearances, and you can still change a single slot, for example to hide your helm or cloak. See Classic or Enhanced preset.
Where to change your look
Blizzard says you set outfits at transmogrifiers in certain cities. Players report them in Stormwind's Mage District, Orgrimmar's Cleft of Shadows and Dalaran in Alterac Mountains. Ask a city guard if you can't find one.
What it costs
Reported: two outfit slots are free, extra ones cost gold that rises the more you buy, and switching between saved outfits is free out of combat. Blizzard hasn't published prices.
For add-ons that help track your collection, see transmog add-ons.