It is weird you brought this up. I myself am getting ready to restore an old 82 Suzuki GS650G that was given to me. I drive a manual car, and I rode mini-bikes/scooters before, but I too didn't know the correct method of shifing a REAL motorcycle... a little bit of internet searching came up with this:
1. Get on the motorcycle.
2. Start the engine in neutral.
3. Squeeze the clutch lever with your left hand all the way to the grip.
4. Place your left foot on the gear shifter and kick straight down to first gear.
5. Give a little throttle with your right hand. Don't race the engine.
6. Slowly release the clutch with your left hand while maintaining engine speed with your right hand on the throttle.
7. Balance the bike and move off slowly.
8. After you are moving and balanced, put your left toe under the gear shifter.
9. Squeeze the clutch and release tension on the throttle a little.
10. Smartly kick upward with your toe on the bottom of the gear shifter. You are now in second gear.
11. Release the clutch smoothly and simultaneously apply more throttle.
12. As you gain more speed, repeat the above steps for third, fourth, and fifth gears.
13. Downshifting is done similarly except you sharply kick down on the gear shifter to go to the next lower gear.
14. As you come to a stop, squeeze the clutch and kick down on the gear shifter, one gear at a time, timing it so you are in first gear as you stop.
1. Practice use of the clutch and throttle together so as not to stall the engine.
2. If you should stall the engine, make sure you have the front wheel straight ahead. Otherwise, you will fall.
3. Practice getting the gear shifter into neutral while stopped. Neutral is between first and second gear.
# The Gear Shift is on the left-hand side of the motorcycle just ahead of the foot peg.
# The Gear Shift controls a ratchet mechanism that shifts the gears.
# Most motorcycles use a 1-N-2-3-4-5 positioning of the gear shift lever with the "1" being all the way down.
# Upshifts from first gear are accomplished by a hard upward thrust with the top of the boot on the underside of the shift lever after first pulling in the clutch.
# The first upward kick from first gear goes through Neutral directly to second gear. The gear shift lever is released after each upward kick. Successive gear shifts upward take the machine to third, fourth, and then fifth (or higher) gear.
# Downshifts occur by pulling in the clutch and kicking down the gear shift lever one gear at a time and releasing it after the shift in preparation for the next kick down.
# There is a complex motion involving the left hand operating the clutch, the left foot operating the gear shift, and the right hand opening and closing the throttle to accomplish smooth shifting both accelerating and decelerating.
Now... if I have missed something or left something out... please let me know...