If you are flying an IFR clearance, the change in course enroute will be minimal -- wait until you see from, turn to new course, set the dial and correct as needed. In a non radar environment, you have to report crossing time to ATC.
In the terminal environment, there will be a procedure turn where a large course change is required -- or you just follow the active STAR. ATC expects you to fly to the fix, then turn. Cutting corners gets you too close behind the guy ahead.