Depending on which version of Savage Worlds you have, the explanation of either starts on P.80 of Explorer's or P. 102 of Deluxe. The short answer is, when you choose the Arcane Background: Super Powers, you immediately gain one Power of your choice and you get 20 Power Points to use that skill. You can take the edge New Power to gain additional powers, which you can take with every advance and Power Points to gain 5 more power points, but you can only buy those once per Level (ie Novice, Seasoned, Veteran, Legendary, and every other advance after that).
Super Powers work differently than the other Arcane Backgrounds in that for each Power you take, it essentially becomes its own skill that you raise with XP just like any other skill. Fortunately, these Power skills are not linked to an Attribute like say Fighting is to Agility, so you can increase two powers per advance as if the skill were below the attribute. The upshot is, if the hero wants to use a Power, they attempt a Skill Roll with the typical Target Number of 4 (don't forget multi-action penalties) either the power works or it doesn't.
I hope that helps.