How do pilots set the exact amount of thrust needed for a reduced power takeoff?
The EMB-145 used a combination of FADEC settings and the thrust levers to select the desired thrust and to signify the need for additional thrust.  

The thrust levers had a detent that selected "100%" thrust for the given mode the FADEC is operating in.  If you pushed the thrust levers past the detent to "max" this would give you extra thrust.  The mode the FADEC is operating in is selected by a button in the cockpit that cycles through the available modes. 

For takeoff power the modes were "ALT T/O", "T/O" and "E-T/O" which gave you 90%, 100% and 107% thrust for takeoff when the thrust levers were in the detent.  If advanced past the detent this would put the mode into a reserve mode and depending on model would give you up to 110% or 117% thrust. 

Setting the exact amount of thrust needed was up to the engine FADEC units, our job was just to tell it what thrust mode it was in and it scaled the output of the thrust levels to that mode.  Flying a 90% thrust takeoff, a normal rated climb and then reducing to cruise levels only required initially setting the thrust levers into the detent and adjusting the FADEC mode.