The “Pistol” is a great exercise to build strength in the legs and hips and it has awesome carryover to any task a soldier uses his legs for. Getting started is a bit of a bear but the tips below will get you there in no time.
The starting position is standing with weight balanced on one leg. The other leg is either airborne or eased out an inch or so above the ground as you descend. More on that later. Just like the one arm push-up, this drill requires high tension.
As you stand on one leg, reach forward with both arms. Tighten all of the muscles in your legs; imagine that you are trying to pull them up into your pelvis. Brace your abs and squeeze your glutes.
Descend by PULLING yourself into the squat with your hip flexors. Pull down and back while keeping your shins as vertical as possible. As you drop down you will have to lean forward to counter balance. It helps to reach for something like a wall or pole that is too far away. If you truly believe that you can reach it you will suddenly find yourself at the bottom of the squat!
Stay tight at the bottom! Take a quick breath, keep the pressure up, squeeze off the bottom and push up into the start. It helps to imagine that you are pushing the earth away from you. You may need to rock forward just a hair, it’s OK.
Switch legs and repeat. Many find it useful to use spiral tension in the leg, trying to screw their leg into the ground. Another excellent method is to use a light weight in your hands (5-30lbs). I use a 16kg KB, which works very well for balance and strength development.
If this proves too difficult, use the Box Squat method by squatting to a chair or box. Gradually lower the level until you are rock bottom. You may also want to just practice the descent for a while before you tackle ascent. A client of mine successfully used the stairs in a pool every day. After a couple weeks he was rock bottom with no problem. The stairs in your house work well too.
On my last deployment I came up with a method of doing assisted pistols with a partner. Face each other with the work legs aligned. Stand far enough apart so you that you can just barely grasp each other’s hand. I prefer fingertips. Descend together and if you start to lose your balance just pull against your partner’s hand or finger tips.