The torque curve
Most motorcycle engines generate peak torque somewhere between half and two-thirds of maximum revs. With your engine sitting at or just below this part of the torque curve, the engine will offer instant, progressive and predictable thrust or assist with engine braking to slow the motorcycle smoothly if you need to. So you need to select the gear that puts your engine speed in this sweet spot.
Being in the right gear, close to maximum torque, is essential for overtaking, giving maximum acceleration when the opportunity is clear.
When cornering, change down the gears on approach so that you turn in with the revs in the same sweet spot, just below peak torque (use the same technique on the approach to a downhill slope). This provides optimum engine braking for turn-in, and perfect linear response as you open the throttle though the exit.
To minimise your chance of ending up between gears in a false neutral, maintain pressure on the gear lever until the clutch has been released. If you do find a false-neutral, change up a gear. Changing down risks engaging too low a gear with a possible rear wheel lock-up and skid.
Some older bikes have the gear lever on the right hand side (some very old ones have a hand change!). Occasionally the change direction can be the opposite of current bikes. Be very careful when borrowing a bike.
Noise selecting first
If theres a crunch of bang when selecting first gear from neutral try holding the clutch in, blip the throttle a little then let the revs drop back to tickover. It can help free the clutch and make gear engagement smoother. Always keep the front brake on until youre ready to pull away.