It might help You to consider the APU a little jet engine (which it is). Just like its bigger relatives, it has a compressor (usually single-stage radial) that feeds a combustion chamber, which in turn discharges into a turbine (usually single-stage radial as well).
The bleed air is tapped from the APU compressor, diverting some air that would otherwise go to the combustion chamber into the bleed air ducting - plain old pipes basically. And these pipes will lead the APU bleed air into the engine starter: as has been explained, this is a little turbine installed on the accessory gear box that will spin the high pressure compressor of the engine. After having passed the starter turbine, the air will typically just be vented overboard.
What You need is a book on jet engine theory. I am sure that a search on common book dealer pages will return several titles in French as well, should You prefer that language.