The pistol squat requires mobility and strength from the entire lower body and core, and once you work up to being able to complete them you can get a great lower body workout anywhere with no equipment.
Most people will not be able to perform the pistol squat properly without working through several progressions that help develop the specific mobility, strength and stability required to get through the exercise for repetitions.
Pistol Squat Progressions
There are two basic ways to progress to a full pistol squat. Either use a progressively lower bench or step, or use something to hold onto while doing a full pistol to help pull yourself up and progressively use it less and less until it is no longer required.
For the step progression, you can use actually stairs or use a chair to start. Stand facing away from the chair or staircase and put all your weight on one leg keeping the other leg straight with the hip flexed slightly so the non-standing foot is held off the ground in front of you. Flex the hips and reach back with your butt towards the staircase or chair and lower yourself down under control keep your arms straight and in front of you parallel to the floor to counterbalance your hips moving backwards. Let the standing knee and ankle flex along with your hip as you reach your butt backwards and go down. However, you MUST keep the heel of the standing leg down and this requires a lot of flexibility of the soleus tendon (soleus is the single joint calf muscle).
Try to lightly touch your butt down to a stair or the chair then drive the standing foot down, squeeze the glute
extending your hip, knee and ankle to the starting position. Perform sets of 5 – 10 reps each leg. Overtime find progressively lower steps, benches or individual stairs so that you are progressively squatting lower and lower until you can perform a full squat on one leg all the way down to the ground and back up again keeping your non-standing leg straight and parallel to the floor while the hip is flexed.
The second option to progress to full pistol squats is to hold onto something that you can pull on while doing a full pistol squat thereby assisting the stance leg. You can hold onto a suspension trainer, a cable machine handle, door frame, chair or table, or resistance training band or rope anchored above you. A great way to do this is to anchor a suspension trainer or resistance band above you to a secure point then grasp the two handles and pull on them as required to do a full pistol squat. Over time progressively use less and less assistance from the upper body, switch to just one hand, then lessen grip and assistance until you can perform full pistol squats.
Videos: https://youtu.be/It3yvU0fomI or https://www.youtube.com/watch?v=PPksQCbeVZw