Instructions
Select a beginner level from the Nexus, as your new character is not very powerful. Level 1-1 and 4-1 work well for farming souls. They are linear and contain numerous enemies near the beginning of the level.
Defeat the enemies in the level to gain souls. Depending on the difficulty of the enemy, the amount of souls varies. For example, the enemies in Level 4-1 are harder to kill, but offer more souls.
Touch the Archstone at the beginning of the level to teleport back to the Nexus with the souls you have collected.
Speak to the Maiden in Black, who is wandering around the Nexus, to upgrade your statistics using the souls you have acquired.
Enter the level again. Upon re-entering the level, all of the enemies reappear, allowing you to kill them again for more souls. Continue to farm for souls in this manner until you are satisfied with your character's growth.