The answer varies a lot depending on the type of plane, but ideally, the pilot will manually apply rudder only rarely.
Rudder will be used to coordinate turns and to slip for crosswinds on landing (if not crabbing). Other than that, the rudder should be trimmed so the pilot doesn't need to manually apply it for straight and level flight.
Some small aircraft lack variable rudder trim; if the trim is not correct, they may need to apply rudder throughout the entire flight--and hopefully fix the trim tab before the next flight.
Single-engine planes will need some right rudder input during full power (e.g. takeoff and climb) due to the left-turning tendency. Multi-engine planes don't have that problem, but rudder is very important when dealing with a failed engine--which should be rare outside training.
A three-axie autopilot will apply rudder as needed to keep the plane coordinated. Small planes may have a one- or two-axis autopilot that requires manual coordination. And, of course, autopilot is not used for the entire flight; the pilot will have to use rudder manually during hand-flown portions such as takeoff and landing.