One-handed:
Trainer - Bonnie
Location - Astrillyn, Training Hall

Two-handed:
Trainer - Xemesis
Location - Valingrad, Training Hall

Unarmed:
Trainer - Lamden
Location - Valingrad, Training Hall

Defence:
Trainer - Sigbjorn
Location - Fraustford, Frozen Reinforcements

Archery:
Trainer - Kelvin
Location - Astrillyn, Training Hall

White Magic:
Trainer - Sven
Location - Astrillyn, Training Hall

Black Magic:
Trainer - Mancano
Location - Bed and Breakfast tavern in wilderness near Valingrad. Coordinates are 366,1535

Gray Magic:
Trainer - Shiraz
Location - Stradynhold, The Sandstone Pub

Lockpicking:
Trainer - Drayden
Location - Astrillyn, The Seaside Tavern

Trainer 2 - Bandit Trainer
Location - Between Margzahn and Heronwood. To the south-east from Ferrynglade and north-east from Stradynhold. Exact coordinates are 521, 1111.

Pickpocketing:
Trainer - Melvino
Location - Valingrad, Valingrad Inn

Trainer 2 - Bandit Trainer
Location - Eastern part of Northwynd. Coordinates are 607, 2049

Barter:
Trainer - Ethelia
Location - Ferrynglade, The Whales Throat Inn

Persuasion:
Trainer - Erin
Location - Valingrad, Training Hall

Alchemy:
Trainer - Lady Christina
Location - Valingrad, Alchemical Supplies

Lore:
Trainer - Stradyn
Location - Stradynhold, The Sandstone Pub

Foraging:
Trainer - Hawk
Location - Heronwood, wilderness. You can find him while traveling from Astrillyn to Valingrad. Coordinates are 543,1674