I've heard two theories, which one is correct?
1. Lift foot off gas
2. Push clutch in
3. Shift to next gear
4. Lift foot off clutch
5. Push foot on gas
1. Push clutch in at same rate as lifting off gas
2. When foot is completely off gas, shift to next gear
3. Now do the opposite step 1: Lift clutch pedal off at the same rate as pushing down gas.
When it comes to numerous Youtube videos/Wikis I've seen both theories explained. I think theory #2 may allow for smoother shifts but theory #1 sounds like it would be easier on the clutch. No matter how gentle you are, in theory #2 it sounds like you would burn up your clutch.
Of course you would need to do theory #2 when getting into first gear obviously.