A gear stick is pretty much just a simple lever. As you move the gear stick the gear selectors in the gearbox move as your motion is translated via a set of levers and rods.
A short shifter or quick shift gearstick essentially alters the throw distance between gear changes by changing the angle/pivot of the lever. They are typically shorter than a conventional stick and can reduce the amount you have to move it by around 40%.
This makes for a much more positive gear change action with each gear slicking into place in a shorter time. With practice the racing gearchange becomes second nature. Every twisty road that requires frequent gear changes will just melt away and you will greatly enhance your driving pleasure.
Most quick shift kits come with full fitting instructions and various, washers, lubricant and bushes. Essential you just remove your gear gaiter, release the old stick mechanism and insert the new shifter and refit. Some cars will need to be jacked up to make the job easier and gives access to the gearbox and underneath more easily.
The downside that comes with a quick shift is that it requires a little more effort to change gear but most drivers will not notice this. If you have a sloppy worn gearbox you may notice that because gearchanges happen more quickly it is a little more crunchy. After you fit a quick shift gear stick you will not want to go back to a conventional one again.