You can read about the Gas-Generator Cycle for rockets here: http://en.wikipedia.org/wiki/Gas-generator_cycle_%28rocket%2...
Basically, a small amount of fuel and oxidizer are bled off into a gas generator and used to power the turbines that feed the fuel and oxidizer into the rocket engine.
The cryogenic fuel is piped about the "outer surface" of the rocket's nozzle and combustion chamber such that these essential structures doesn't melt away under the pressure and heat.
I do find that a brave integration -- using fuel as a coolant.
Not an engineer in this field, but I'd imagine using fuel flow as coolant makes for a lighter-weight engine overall, even as it might complicate control system software, and might place narrower limits on, or complicate stability control of the engine's net available (throttable) range of power.
Just speculating here, but perhaps a single engine's power range limitation becomes another reason (along with graceful system degradation, without mission loss, under single engine loss) for SpaceX's multiple engine designs for their larger rockets? Switch off additional engines as rocket weight decreases (due to fuel and oxidizer usage) during descent? Doubtless there is a great difference in total mass between take-off weight and landing weight, so it would seem to require a lot less fuel & oxidizer to land it than to lift it to orbit.
Also wondering about ablative heat-shield placement and arrangement for re-entry, first and second stage.
The fuel is used as coolant since it's a better coolant than the oxidizer for a range of reasons. One of them is that hot oxygen is very corrosive. Also, because of that a small oxygen leak from the coolant passage to the chamber tends to grow larger with catastrophic consequences. With kerosene the problem is coking.
Yes it's more complicated to design a regenerative cooled engine, but existing materials can't take the heat. Some maneuvering thrusters are heat sink designs. Some engines are ablative, with things like evaporating carbon taking the energy.
Yes it only needs one engine for landing vs nine for fully laden takeoff.