Ok basic acm operation:
bleed air from the engines or apu or indeed a ground source is fed to the packs by the PFCV's (pack flow control valves). From here it passes through the primary section of a dual heat exchanger where the cooling process begins. The air is then compressed in the compressor section of the ACM and cooled again as it passes through the secondary section of the dual heat exchanger, then the temperature of the air is greatly reduced as the air expands across the turbine (in the ACM) which being mechanically coupled drives the compressor. (bootstrap cycle!), but, as not all the heat needs to be removed from the air a turbine bypass valve controlled by a pack temp controller bypasses some of the air that would pass across the turbine, this will reduce the need to later add trim air to the zones.
The bleed air will start off with a temerature (depending on aircraft and engine type) of around 350f (180c) and the ACM will easily drag this down to typically 0c, some systems can get ice rattling around in the mix manifold (plenum) if the control system loses the plot!!. Some packs have the addition of a fan driven by the comp/turbine of the acm that is for use on the ground to increase the airflow across the heat exchangers. Other refinements may include moisture removed by the water separators being sprayed into the inlet to the heat exchangers to increase cooling through evaporation. The packs, controlled by the temp. contollers will control to the cabin zone with the least heat requirement and hot trim air will be added to the ducts feeding those zones that require more heat to get the cabin (zone) temperature to the selected level.
Nice diagramms here for the 737
737 site