It's actually reasonably easy to explain. The extraction is much the same as any contemporary rifle, regardless of action. The fresh round, when stripped from the magazine, has it's rim slide under the spring-loaded extractor hook.
When the action cycles, the extractor drags the case from the chamber as the bolt moves to the rear. At the appropriate point, the opposite side of the case-head strikes the ejector, and is booted out of the ejector opening.
The bolt itself is a gas-operated turn-bolt system, incorporating a two-piece bolt (the bolt head itself, with it's locking lugs, and a carrier, which has the camming surface. When the weapon fires, gas is tapped off through a small hole in the barrel and travels back to the bolt through a tube.
The pressure forces the bolt carrier to the rear, which makes the cam surface turn the bolt head far enough to unlock from the breech.
Traveling to the rear, the bolt assembly performs the ejection chore described above, and also re-cocks the "hammer".
The recoil spring then drives it forward, stripping another round from the magazine to repeat the process..
A decent animation of the process:
http://www.youtube.com/watch?v=FZipq6D6D9k