From Dungeons of Dredmor Wiki
The player is able to choose 7 skills upon starting a new game. These are the skills the character will have for the duration of that characters life-- new skills cannot be learned, and the ones chosen cannot be changed once in game.
Whenever you gain an experience level you gain a skill point, which can be used to advance one of your skills. Skills have 5-8 levels of advancement.
To create and vote on skill builds, see: Strategy.
For a simple breakdown of the skills, (incomplete) see: Basic Skill Strategy.
 Vanilla Skills
 DLC Skills - Realm of the Diggle Gods
 DLC Skills - You Have to Name The Expansion Pack
 DLC Skills - Conquest of the Wizardlands