What is the throttle setting of a piston aircraft during cruise?
Broadly speaking its what ever you chose it to be. You should always refer to your aircrafts POH for the information specific to your airframe and engine. Beyond the POH there may also be supplemental engine information from the maker.

Generally take off and at least initial climb out occur at full throttle. Then at when you reach your cruising altitude you will throttle back to your cruise power setting and level off. 

For example lets take a look at the charts for a PA-28 

You can chose your desired power setting based on a desired fuel burn 


Then refer to this chart to see your airspeed. 


You can then use these numbers for your flight planing, or work backwards to achieve a target airspeed. 

For a trainer these numbers tend to be not all that large of a range. My Archer will do a full power climb out at 2650RPM then throttle back to about 2450RPM for cruise. Higher performance aircraft may have larger ranges as well as more complex operating limitations. Some engines have time limits on which they can be at full throttle and most have thermal operating limits if you decide to dance on the mixture lever. Turbo or super chargers may also add an additional level of management to prevent over boosting. Modern digital engine analyzers allow for a level of precision previously unachievable. 

AOPA has a decent article on power management over all, you can find it here.

Pro Tip: A lot of small trainers print the engine performance data on the inside of the sun shade so you dont need to thumb through the POH in flight.