The pistol, or single-leg squat, is a unique exercise that combines strength, flexibility, and coordination.
The pistol squat puts all your weight on one leg, making this exercise much harder to perform. It is a great bodyweight exercise if regular squats or lunges became too easy, and it allows you to build massive leg strength without putting a heavy barbell on your back which compresses your spine. But it is not only a progression of the squat, in fact, it works your body in whole different way. You will require much more stabilizing muscles to keep yourself balanced on one leg and require a lot of hip, knee and ankle mobility. The pistols will also help you to correct strength imbalances between the legs, because one leg cannot compensate for the other.
This is an Intermediate exercise, most people won't be able to do even one full range pistol squat at first, and even people who can squat heavy weight cannot perform them sometimes, because it requires a different set of abilities. You should be able to do at least 40 bodyweight squats before considering the pistol squat.
Although the pistol squat will strengthen your legs, it is not a bodybuilding exercise, but its a movement exercise. The main purpose of the pistol squat is to move all the major muscle groups together, rather than targeting a specific muscle for hypertrophy. The pistol squat will improve your ankle and hip mobility, improve flexibility and increase your balance tremendously.
To build your strength up if you can't perform a full pistol yet. Start by doing regular bodyweight squats, you should be able to do at least 40 reps. After you'll get better, it is recommended to practice the squats with very narrow stance, when the feet are close together. Then do a pistol squat holding a pole, gradually decreasing the amount of assistance the pole provides. Then progress to a single leg box squat where you lower yourself on a box or chair instead of the floor. Gradually decrease the height of the box.
Watch your knees. One legged squat requires a lot of mobility and stability from your knees. If you feel pain or bad balance in the knees, work on their mobility first and do assisted pistols.
Don't let the knee to pass your toes. This will put too much stress on the knees, your knee should be directly over the toes at the bottom position.
Keep your heels on the ground. Ankle mobility tends to be one of the most common problems preventing people from doing the pistol. To avoid overloading the knee joint, keep the feet flat on the ground. If the heels begin to raise, work on your ankle flexibility.
Its ok to round your back at the bottom of the movement. Since your back doesn't have to carry any weight, it is ok to round it at the bottom, trying to keep a neutral spine at the bottom position might be too difficult to achieve.
You can use a counterweight to help you with balance. Hold a dumbbell, kettlebell or a plate in front of you as you squat, the counter weight will help you to keep your balance. Gradually reduce the weight until you can do the pistol squat without it.