Manual Rear Wheel Drive Cars
Depress the clutch, and rev the engine.
In one quick motion, "dump" the clutch and press the brake pedal while flooring the gas.
Use a line locker. A line locker is a device that modifies a car so the brake pedal only engages the front brakes. This dangerous and usually illegal device makes burnout on RWD cars easier and more dramatic. A line lock is a solenoid (fancy name for a switch) that gives you some extra buttons in the drivers seat to control your brakes. To do a burn out with a line locker installed:
Step on the brakes.
Push the line lock button.
Release the line lock button leaving your front brakes on and disengaging your back brakes, leaving those wheel free to spin, burn and make smoke.
Push line lock again to release the front brakes and move forward.
Do a donut. A doughnut (donut in the USA) is a circular burnout. To do a donut in RWD cars:
Find a large open area with no other cars, lampposts or other things you can hit. It is easy to lose control of a car with a donut.
Begin driving in slow circles.
Hit the gas hard so that the rear tires begin to lose traction.
tips
If the engine stalls you haven't revved the car high enough before popping the clutch, or your vehicle doesn't have the power to burnout.
To test if your car has enough power nail the gas from a stopped position and see if you can spin the tires.
An alternative to a line lock is a "Brake Clamp". Designed to clamp off a brake line when being worked on, these can also be used to shut off the rear brakes thus allowing only the front brakes to function when the pedal is depressed. Note: most cars have a steel brake line from the brake booster to the rear of the car, the area to put the brake clamp is a short length of rubber hose that attached to the Differential. (some cars have two separate brake lines, one for each side, in which case two brake clamps are required.
Try changing your tires. The worse your tires are the easier it is to make them spin, plus they smoke easier and you will not ruin your good tires.
Increase the amount of smoke by lubing your drive tires with old motor oil.
It can help to give the tires a quick powerful spin before pulling the e-brake.
Pouring bleach on the area where you plan to burnout will help create more smoke.