Downshifting while slowing, Famine explains it well. Clutch, bump the throttle for some revs while selecting the next gear down, and releasing the clutch as the engine coasts down to the revs needed for the gear. Done well, there is no lurching forward or dipping the nose as you shift. If you're stopping, don't bother with all of that. It's unnecessary and annoying to your passengers. Just coast, depress the clutch as the car slows, and get neutral for while you sit at the light. If you're slowing for a turn, again don't worry about every gear on the way down from 5th to 2nd. Slow, use the clutch, shift straight to second, give it enough gas to come out of the turn and release the clutch, drive on your merry way.
Downshifting to drop a gear and nail it, it's still pretty much the same, but no "coasting." Once you've learned the car's rev ranges and gearing, you can downshift while giving throttle, and nailing throttle as the clutch is engaged, and accelerate away, on your passing maneuver or whatever.
While learning, always complete your shifts before giving a lot of throttle. Your (or whomever's) car and clutch will last longer, and people won't begin to fear riding with you. As you get experience, you will develop muscle memory and a feel for where the revs are for each gear, how much space there is if you drop one gear or two gears, or even three gears. Don't try to watch the tach and think, "I was at 2500 RPM, and I need to be at 5,000 when I release the clutch." You'll drive into something that way. Use your ears, and listen to the engine.
Most importantly, you don't want to slip the clutch very much, which is the whole point of rev-matching. If the engine is turning quite a different speed from what it would while in the gear you're selecting, then the clutch has to absorb that difference through friction, and thus wear. If the engine's way too slow, letting out the clutch drags it up to speed, and jolts the car a bit as if the brakes had been tapped. If the engine's way too fast, then the clutch is slipping to drag the engine down to speed, and if severe enough, snapping everyone's neck back as the car lurches forward.
All this assumes a traditional H-pattern stick. Sequentials are different. And there are a few sequentials out there with clutch pedals, not just paddle shifters.