A Climbing Speed can be used to move on a vertical surface without expending the extra movement normally associated with climbing.

A creature in general needs BOTH hands to climb.

Some creatures have the Spider Climb Effect, which allows their Climbing Speed to work even on the underside of horizontal surfaces. If they have this status effect, they do not need to have both hands to climb, they simply climb with their feet.

Creatures without a stated Climbing Speed move at half speed.

It is then up the GM to determine if Endurance or Balance should be used. Sheer surfaces have a DC of 20, while difficult surfaces with grips or objects to grab onto should have a DC of 15.