How do black holes evaporate?

The evaporation occurs through Hawking radiation. This is a very slow and low energy process. So low that the cosmic microwave background radiation, which is just a few degrees above absolute zero, pours far more energy into the black hole than Hawking radiation takes away. So in principle a black hole cannot evaporate.

With the exception of conjectured atomic sized black holes, that is, as Hawking radiation would be more pronounced then.

Edit: See this answer on the physics SE: http://physics.stackexchange.com/a/26607/55483
The black hole would need to be less massive than the moon to radiate more energy than it absorbs. Bigger than atomic size, as I suggested.