98.5_SVT,
Beyondloaded summed it up. Most of the rest introduced other terms that are different, but possibly related or can be used together. The goal is to rev match with every gear change, up or down. The jerking is because the engine speed is not matched to what the selected transmission gears/axle/wheels are turning. This jerking could occur no matter what gear to which you are shifting, up or down. By nature, upshifting tends to be smooth without most poeple not knowing why. Downshifting requires an extra effort, raising the engine speed vs. the speed it was at in the higher gear. You can calculate all the appropriate engine speeds for every mph in every gear so that you cna always know what you need to bring it to, but experience and feel are the only ways to make it smooth. Use momentum of the engine going up or down to help make it smooth, yet minimize clutch slipping. Quick blips of the throttle when downshifting work well, but you must do it by the right amount.
Practice, pratice, practice. Maybe watch some others that are more experienced with rev matching.
Combining rev matching with heal and toeing or double clutching can be very useful to make the shift smooth and/or reduce wear.
Keep in mind that downshifting is not an effective braking tool. Even if you do it "right" and minimize engine/tranny/clutch wear, the momentum of the engine speed is not going to slow you down quicker than the brakes would. In fact, quite the opposite in emergency/racing braking. It is effective in setting you up with a desired gear for maintaining the corner speed and power out of a corner. And for certain vehicle, the sweet sound of the engine and exhaust make it fun.
