Each successful player has his or her own individual stance at a pool table. Nevertheless, all are variations on a common theme--the basics of a billiards stance are the same for all regardless of experience, weight, height or age.
It begins with the placement of your feet. You cannot have a steady hand unless you have a steady base. Like in any sport that requires you to stand, it is crucial to place your feet not too far apart yet not too close together, in a stance that creates a comfortable and sturdy base. Experiment, and find a position that works for you. After you find it, the next task is to incorporate that base into a stance suitable for playing pool.
A player's center of gravity changes when leaning over to shoot. To account for this you may need to adjust your feet slightly while bending at the hips, but you still should place an equal amount of weight on each foot. Your bridge hand is not for leaning on the table, so your weight needs to be completely controlled by your stance.
For a right handed player, the right leg (back leg) is relatively straight but not locked straight; locking your back leg causes tension in the leg muscles, which can result in fatigue and weakness. Your left leg needs to bend at the knee, which allows an easier bend at your hips toward the table.
Some players are very flexible and bend easily at the hips. Those who are less flexible must compensate by bending their front knee more or widening the stance an inch or two. Both methods lower your body just the same as bending at the hip. The point is to put the rest of your body in a proper position.
Getting the rest of the body in a proper position is the goal of everything you have read up to this point. Where should your arm, head, bridge hand and even your eyes be? Almost every successful player has a few things in common from this point forward.
The forward arm, with the bridge hand, is always nearly straight. Not uncomfortably straight and locked at the elbow, but extended out away from your body. One reason this is done is stability; your body is in a sturdy three-point stance, more solid than a two-point. Also, keeping your arm straight makes you less likely to bend your elbow and rock forward when shooting.
The back arm or more specifically the back hand placement on the cue is critical to your success. The correct place to grip your cue is the place where a line drawn from your elbow to your wrist points straight down to the floor. This is the hand position you want when the tip of your cue is within an inch of the cue ball. This pendulum thus created (elbow to wrist) can move freely forward and backwards. It also allows your bicep and triceps to be completely relaxed, until you take your stroke. It helps to practice this by getting in a shooting stance without a cue. Swing your elbow forward and backwards without dropping your shoulder. Relax your elbow while holding your shoulder firm. Gravity will show you the natural point straight down. You have created the pendulum.
Your head position is a result of everything you have done up until this point. Watch the great players. What you see they have in common is they are looking straight over the top of the cue. In most cases their chin is no more than 6 inches from the cue. When they do their practice strokes and shoot their head never moves. The result of an effective stance.