On page 4 of this excellent thread, Keith asks why the gearstick on most racing cars years ago was on the right-hand side. It's simply because there is nowhere else for the linkage system to go. In mid-engined cars, the engine is in the way.
Linkage systems differ, of course, from one manufacturer to the next, but in principle, they serve the same purpose. Usually, a rod is run from the base of the gear lever, and is positioned alongside the right of the engine. It is attached to the gearbox, normally at the rear of the casing, and operates on a 'push-me pull-you' principle.
Most I've used are 'orrible at first, but you soon get used to them. It helps if, like me, you were brought up on severely neglected farm tractors and Land Rovers. I used to think it was normal to stand on the grey Fergie's gearstick to change from bottom to second... It isn't.