What coffee king said.
Normal driving in a normal modern car:
1)clutch in, engine disengaged from gearbox input
2)shift to neutral, there are now 3 parts to the system moving independantly, the engine and flywheel, the clutch plate and gearbox input shaft, the output shaft of the gearbox.
Depending on design theres alos various dog gears, lay shafts etc, but we'll ignore those and just assume its a 2speed+reverse in a nice simple box.
The output shaft spins at the road speed.
The engine spins at whtever you let it.
The input shaft stops (not entirely, but 'box oil is pretty thick so its slowed enough compared to the 6000rpm+ it was doing a split second ago and thr 4000rpm you want it to do after the upshift)
3)Shift into the next gear and the two gears (output and input shafts) are at different speeds, to you have 2 brass 'cones' between them, as you push them together the input shaft speeds up, the further you get towards the gear the faster it spins untill they match just as the gears are about to engage.
4)Hopefully the engine revs now match your road speed (you've been off the throttle a split second) so when you relsease the clutch the input shaft is moving the same speed as the engine an everything is nice and smooth.
double clutch method
As above, but,
After (2), release the clutch quickly and press it again, this conects the input shaft to the engine again and gets it spinning, as the pedal comes up push it into the new gear, as both are spinning the syncro cones do no work, and everything meshes smoothely.
Basicly the clutch slips rather than the cones, and if you've ever tried clutch plates are easier to change than a gearbox rebuild.
TBH, I've never bothered, even in the midget, full throttle, clutch down about 3/4 of the way (to the bite point so the input shaft never stops spinning), next gear, revs have rissen as the load came off the engine so the flywheel gives the whole car a kick up the arse as you let the clutch out.
). You'll find the decisive movement is better than being light. It doesn't require much force on a dog box but on a standard synchromesh box you have to use enough force to get past recalcitrant cones that are trying to do their job. That's a firm shove.
