Check the performance graph in the tuning page for the car you're driving to see where the maximum torque can be achieved. Use that RPM range as a reference and experience with it (+500rpm or -500RPM) to see which RPM is best to launch the car off the line. Once you find that sweet spot, hold it, dump the clutch and floor the throttle.
That's what you're supposed to do IRL. However in the game, if you watch the example video of Gold license time, the AI red line it off the line every time.