I will now take the liberty of answering my own question, almost in full (I'm missing or forgot the details for a few).
Aethra
Location: Citadel, Seminary
Trains: Literacy and lore
Requirements: Pay a fee
Aufinius
Location: Barrier, the square or Kaliyan Inn, depending on time of day.
Trains: Speech
Requirements: Talk to him at the inn. May need to pay a fee, don't remember.
Dinali
Location: Barrier, Kaliyan Inn
Trains: Blunt or Unarmed
Requirements: Find his fiancee, Meila, in the square. She will have you go to Dinali and remind him that he's supposed to be meeting her. Sometime after delivering the reminder you will find them both at the inn, and Dinali will offer you training if you talk to him.
Gralinus
Location: Citadel, House Char
Trains: Any weapon skill or Armor
Requirements: 1000 drachs or for free as a reward from Lucien for helping House Char.
Larvo
Location: Citadel, southwest quarter
Trains: Pickpocket
Requirements: Talk to him, catch him pickpocketing you, then as recompense demand he train you in pickpocketing.
Nurens
Location: Barrier, (Haven't Found)
Trains: Literacy and lore
Requirements: (Haven't Found)
Ragnard
Location: Monastery, eastern plaza thingy.
Trains: Power of Flame
Requirements: None.
Telus
Location: Barrier, Gem Shop during day and Tarsh's Tavern at night.
Trains: Barter
Requirements: Talk to him at the gem shop and ask him to train you, then go see him at the tavern at night and he will train you for a fee. WARNING, do not accept his training until after receiving Component 1 from him for the Rebellion, as once you get training from him the game assumes any further attempts to talk to him are just to thank him for training, and you will have no dialog options other than "Goodbye".
Temiani
Location: Citadel, southwest quarter
Trains: Music
Requirements: A fee and possession of an instrument (though he will sell you one if you don't have one).
Thonmil
Location: Citadel, locksmith
Trains: Tinker
Requirements: 25 drach fee
Una
Location: Barrier, don't remember where
Trains: Medical
Requirements: Possibly a fee.