Attribute Points are earned through two different methods. Breaking a Luminous Visage gives you a free level up and an attribute point. There are 15 per playthrough to find. Normal levelling occurs by feeding souls to Vulgrim who you unlock after defeating the first boss and heading to the large tree in the city.
Feeding Vulgrim enough souls levels up Fury and each level up unlocks an attribute point. The Attribute point is earned automatically but must be spent in the character menu and can be spent on one of the 3 basic attributes: Health, Physical Damage or Arcane Damage.