How long does flight planning take / when is it done / how is it done?
The pilots don't do the flight planning. It is done 1-2 hours before the flight by dispatchers using computer software.  

On a quick turnaround, one pilot goes to a printer to retrieve the flight plan. The other stays with the aircraft and prepares for the next flight.   

Sometimes someone will bring the flight plan directly to the aircraft. Some airlines have stopped using paper flight plans and instead download to an iPad. 

The pilots review the flight plan to ensure it meets all requirements, and can request a reroute, or additional fuel it they feel it is needed.