Skills can be unlocked upon reaching certain character levels, after investing a certain number of passive points into a class, or after selecting a Mastery Class.
Opening the Skills Window (bound to the S key by default) allows you to see which skills your character can unlock, and how to do so. You can also click on any skill to view its Specialization Tree.
Clicking one of the 5 skill slots on your Action Bar at the bottom of the screen allows you to change which skill is equipped there.
