Summarize:

In many go-karts, you can only brake with your left foot. Other go-karts give you the option. Either way, braking with your left foot can give you a split-second advantage over other drivers. Breaking with your left foot saves you the time that it takes to switch from the accelerator to the brake and vice versa. If you're used to driving a car, you typically brake with your right foot. That means it's going to take some practice to become proficient at braking with your left foot. Spend some time practicing on the track before you race. Go out on the track when there are few cars, and consciously think about using your left foot to brake. Place it on the brake throughout your drive so you remember to use it. If you can't seem to get the hang of it, switch back to braking with your right. If you're only so-so at braking with your left, then that's worse than just doing it with your right. If you're jerky with your brakes, you're just going to slow yourself down. Slowly press down on the brake in 1 smooth motion, and then release as needed. In other words, don't punch the brake multiple times to slow down.
Work on left-foot braking. Practice with your left foot to get better. Hit the brakes as smoothly as possible.