This question comes up enough that it's worth a dedicated thread.
The goal is to re-start the engine at the end of an engine-off coast, while the vehicle is still in motion. You want to impart as little shock/wear to the drivetrain / passengers as possible.
Don't ...
- ... don't simply dump the clutch in the gear you plan to use. Not smooth! It's hard on the drive train & potentially dangerous depending on the circumstances (sudden engine braking of the drive wheels).
- ... as with other advanced techniques, DO NOT try to learn this in traffic! Learn on a deserted road or a parking lot where there's no traffic.
Do this instead:
- 1) select a higher gear than you would otherwise be in for the vehicle's current road speed. (EG. I'll typically select 5th to clutch start at speeds where I'd normally be in 3rd, 4th where I'd normally be in 2nd, etc.)
- 2) let the clutch out part way, smoothly & relatively quickly, only as far as needed to spin up the motor
- 3) immediately depress the clutch as soon as the engine spins up
- 4) select the appropriate gear for your current road speed
- 5) "rev match" before releasing the clutch again - that means, blip the throttle to bring the engine speed up to match the transmission speed before smoothly re-engaging the clutch.
Note on (1): you obviously can't select a higher gear if you're already traveling at speeds where you would return to top gear anyway. But you should still do the "partial" clutch engagement and immediate dis-engagement to restart the motor, and the rev-match to re-engage the clutch.
Note on the first "don't" - one instance where you might simply dump the clutch in the gear appropriate for your road speed is if you need the engine on NOW (maybe for safety reasons), and the extra 1.5 seconds to switch gears & rev match would take too long.
With practice using this technique, "bump" starting should become a misnomer. Clutch starting the engine in this way should be nearly imperceptible to a passenger.