By your phrasing I take it you doubt the moon landings for some reason? Fine. I can help by explaining some of the hardware used.
The Apollo space suits were known as "A7L" suits (google it for more info). The life support back pack was known as the "PLSS" (google that too, and you can find some pretty good images and very lengthy technical pdf documents).
The PLSS was powered by a silver-zinc non-rechargable (aka "primary") battery manufactured by
EaglePitcher. They still make batteries for military and aerospace applications.
PLSS Battery:
25.4 Amp-hours (Ah)
16.8 Volts dc
PLSS usage rate: 2.7 Ah
http://next.nasa.gov/alsj/a17/a17lspSect4.4.pdf
Diagram showing where installed:
http://www.hq.nasa.gov/alsj/plss103.jpg
The silver-zinc battery chemistry has the highest power/weight ratio of any battery in production, but they're very expensive.
[qimg]http://www.cotsjournalonline.com/img/archive_images/cots0805/cots0805sd_zp2.jpg[/qimg]
http://www.cotsjournalonline.com/img/archive_images/cots0805/cots0805sd_zp2.jpg
In large sizes they are used in satellites and helicopters (rechargable) and torpedoes and missiles (non-rechargable). The smallest sizes of the silver-zinc battery are sold for hearing aids.
All the batteries in the Saturn IV stages, Command Moduel, Lunar Module, PLSS and Lunar Rover were silver-zinc primary batteries of various sizes.
The Apollo suit and PLSS technology lead directly to the development of the current space suits used by Shuttle astronauts.
I can also explain the cooling system further if you're curious. Or you can google it -- key words
PLSS sublimation plate