How do space shuttles generate electricity?

[nuby]

From what I understand NASA shuttles use electrolysis in fuel cells (their fuel cell power plants) . But how does it work? Do they bring up liquid oxygen and hydrogen, or is it something else with water? What is the byproduct?

 

[Mech_Engineer]

They use on-board tanks of hydrogen and oxygen to run through the fuel cells.

http://science.ksc.nasa.gov/shuttle/technology/sts-newsref/sts-eps.html

 

[nuby]

and if water is the by-product, why do they still need recycle bodily fluids to drink?

 

[mgb_phys]

The shuttle doesn't however the space station does recycle urine and humidity from the air.
The shuttle has relatively short missions and gets most of it's power form fuel cells, the ISS has more man-days to supply and gets most of it's power from solar panels.
In addition developing and testing recycling is part of the research program for longer term space exploration