Cabin pressurisation, temperature control and breathing air are all part of what is know as cabin conditioning. I could write a whole book here, and only scratch the surface. So I wont

There is a mixture of correct and almost correct information in this thread.
The aircraft takes off. Pressurisation begines at 300 feet and is progressively increased with the climb. This figure of 8000 feet cabin altitude pressure, though correct, you will not reach that pressure until the aircraft is at about 20000 feet. As I said, it is progressive. Pressurisation also ends at about 300 feet on approach. The aircraft never lands pressurised. In the event of an emergency evac, cabin pressurisation will put up to 8 tons per square inch on a door. (it always makes me laugh when the papers wet themselves with a story about a passenger who tries to open a door in flight. Arnie and the whole of WWF would not be able to open the door), so for this reason it is dumped. Also I can tell you, being in a pressurised aircraft on the ground is a very, very uncomfortable sensation. I hate doing cabin pressurisation tests.
The short version of the system is.
Air bled from the compressor (the 737-800 from 5th and 9th stage depending on engine speed)
It is very, very hot even though it has come from the compressor (it does not matter if you are on the ground of 30,000 feet, it will burn) it needs to be cooler. It is cooler by the precooler using fan bleed air.
It then passes to the packs. They cool the air, compress it, cool it again and then the water is extracted from it. This water is then sprayed into the heat exchangers to increase cooling efficiency. Once it has passed this it is then heated up to the required temperature using the pack air that is tapped off before it enters the Packs. Once heated it passes to the mixing manifold where it is mixed with recirculated air and then pumped into the cabins. A direct result of this is pressurisation. That is controlled automatically (and with manual backup). At the back of the aircraft we have an outflow valve. This is electrically modulated to maintain a set bleed of air from the cabin in accordance with the altitude of the aircraft. Also we have overpressure valves and negative pressure valves that work in the event of, well what they are titled.
Regulations FAR and JAR sttre that fresh air must be provided at about 0,283 cubic metres or 0,35 kg per minute. So for a 737-800 an air flow of about 70 to 90 cubic metres per minute is required.
This is a short and simplistic version. If anyone is interested, I have systematics of the system.
Matt
"A bit of a pickle" - British translation: A catastrophically bad situation with potentially fatal consequences.
PETA

People Eating Tasty Animals.
B1 (Cat C) licenced engineer, Boeing 737NG 600/700/800/900 Airbus A318/19/20/21 and Dash8 Q-400
1. Captain, if the problem is not entered into the technical logbook.........then the aircraft does not have a problem.
2. And, if you have time to write the fault on a napkin and attach to it to the yoke.........you have time to write it in the tech log....see point 1.