This is my son Justin's Go-cart. I built it myself. It started out as a frame I built and had a 2hp Briggs side shaft engine with a centrifugal clutch driving one wheel, as most go-carts are.

We recently upgraded it to a 4hp engine, using a vertical shaft to transfer power to a 5 speed gearbox(plus reverse).
It has a centrfiugal clutch mounted under the engine, that drives a chain connecting it to the transmission, which has a chain connecting it to the axle that drives both rear wheels. To "go" you just hit the gas. The clutch engages and the cart moves. TO stop just hit the brakes. To change gears you select a gear from the shifter to the left of the driver. Gear changes are not very smooth under throttle but if you back off just a bit it shifts great on the fly. It runs about 20mph.
Here you can see the shifter handle.
Did I mention he's only 5 years old? He's already a great driver!