Doing a burnout in a car is not as easy as most people think. Anybody can light up the tires as they drive away, but it takes a little more skill to spin the tires while the car is stationary. Unless your car has a line lock feature, there are two ways to execute a burnout. The first is to use heel and toe and the second is to use left foot braking. No matter how you do a burnout, the first step is to ensure that traction control, stability control and ABS are fully disabled beforehand.
Once the electronics have been disabled, you are ready to do burnout. For the heel and toe method, you will want to push the clutch in, put the car in first gear and put half of the ball of your foot on the brake to apply brake pressure and then roll your foot so the other half of your foot can keep the revs up so when the you dump the clutch, your right foot is both holding the brakes and applying power. There is some variation in technique depending upon your feet and the spacing of the pedal box in your car. Sometimes it is easier to use your toes to apply brake pressure and swing your heel over to apply throttle which is where the name heel and toe comes from.
The second approach is to use left foot braking. Once again, use your left foot to clutch in, put the car in first gear but this time your right foot is only used to apply throttle. Then bring up the revs, dump the clutch and as quickly as possible, get your left foot over to the brake pedal to keep the car in place. Keep in mind that the car will move forward a few feet in the time it takes to get your left foot from the clutch to the brake. The upside to using left foot braking is that you have a lot more control. Left foot braking allows you to modulate brake pressure as you are doing a burnout. Easing on and off the brake allows you to stop the car, then start the car, and stop the car while doing a burnout.
This method is a little harder on equipment because once you stab the brake pedal, it puts a lot of sudden resistance on those spinning wheels which can result in a broken driveshaft or axle. These risks can be minimized if you do a burnout on a loose surface like gravel or snow as opposed to pavement. No matter how you do a burnout, it is hard on tires, driveline and rear brakes. Because of these risks, it is recommended to start practicing on loose surfaces like snow or gravel before moving to pavement. Have fun!