You kids with your fancy syncromesh single-stick gearboxes. I remember back in my day when we had different gear levers for different gear sets, and when you didn't shift smoothly the transmission would let you know. The straight-cut gears act as the gearbox bouncer and you better be smooth if you want to get into the club. There was no rev-matching by way of a computer or fancy paddle-shifted dual-clutch units when I was a kid.
Okay, so I'm only 32, but I've experienced plenty of older transmissions in my day. The best way to tackle an older gearbox is to understand the art of double clutching, also called a double-declutch shift. Essentially, you clutch in and out when coming out of and into each gear. So there are two clutch movements between gearshifts. On downshifts, you have to add in a rev match by giving the throttle pedal a few love taps.
It's easy to explain but harder to do. Once you see it in person, however, it all makes sense. Pretty handy then that we have a video that perfectly explains the process. Check it out.