Strength
Grows per hit, with any weapon, always the same amount. Each level adds +1 damage to every swing: strength 10 means +10 damage per hit.
Vitality
Grows by taking damage. Increases max HP and regeneration.
Agility
Grows by running and dashing. Besides moving faster, it increases the attack speed of every weapon.
Stamina
Also grows only by running — slower than agility. It sets max stamina, not regeneration.
Weapon skills
Each weapon has its own skill, growing per hit with that weapon. Each level adds +1 damage with it. Damage does not change XP, so a fast light weapon trains fastest.
Board example: strength 10 + longsword skill 20 + a 20 damage sword = 50 damage per hit.
Blacksmithing
Grows by forging with the right materials. Visible jumps at levels 25, 50 and 75, and results vary with the ingot.
Cooking
Not implemented yet.