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Very often a virtual particle–antiparticle pair appears and because they're very happy they started existing, they immediately hug each other not knowing that will cause them to annihilate each other and disappear.
Every once in a while, the pair appears in a very interesting position: one is outside the event horizon of a black hole (let's call this one Pinocchio) and the other inside it (let's call it 3735928559). Because nothing can escape a black hole, they can't really hug, so Pinocchio says "I'm a real ~~boy~~ particle" and stops being virtual and becomes real, while 3735928559 continues its descent into ~~madness~~ singularity.
Unfortunately, the process means there now exists something (Pinocchio) where there wasn't anything before and that takes energy. And that energy comes from the particle that stayed behind which is now part of the black hole, so it effectively takes energy out of the black hole. You may have heard that energy cannot be created or destroyed, only transformed, that's essentially what happens here.
The Pinocchios go away from the black hole, so they can end up basically anywhere in the universe.
As for the timescales, they entirely depend on the black hole's size. Really tiny black holes evaporate in a matter of seconds, the supermassive ones in a matter of trillions of trillions of trillions of trillions... years.
In fact, black holes will be the last macroscopic structures to exist in the universe because the evaporation is extremely slow - every planet and every star and every gas cloud and every atom will cease to exist long before the last black hole evaporates.
How does adding a particle to the black hole remove energy from it?
It's not a particle in the regular sense you might know, like an electron. The pair that comes into existence is meant to annihilate immediately (meaning there's zero energy gain or loss) but because of where it appeared it can't.
When it appears as I described, there suddenly exists a real particle in the universe outside the black hole, so the universe gained +1 in energy.
But energy can't be created or destroyed, so that +1 means somewhere there must be a -1. And that somewhere is the black hole which caused the particle to exist in the first place by swallowing its pair.
It's not very intuitive, that's the fun part about quantum mechanics: nothing is intuitive.