One of the most basic ways to create stability is to use opposing muscles against each other to stiffen and stabilize a joint.
The idea here is not to exert as much tension as possible but to use the amount of tension that is just right for the task at hand.
Why? Because the more tension that we exert the more we impair sensitivity, awareness and adjustability. Plus it uses more effort than when just the right amount of tension is used.
Plus the ability to vary the amount of tension, from too little, to too much, leads to better control of the body, the chance to make fine adjustments or the chance to control movement so that it is slow, smooth and gradual if that is desired.
Another way that stability can be created is to use muscle power against the force of gravity. In this case, instead of muscles working against each other, a set of muscles works against the weight of the body part it is supporting.
Those muscles are then working against gravity.
A simple way to turn yoga poses into stability exercises is to shift foundations. That can mean lifting a hand that is resting against part of the body or the floor, or it can mean lifting a leg. It can also come by repeatedly adding weight to a yoga pose and then subtracting weight. This can be done by lifting limbs in such a way that the pose foundation has to work harder to support the extra weight.
In yoga poses like triangle pose or side angle pose the arm rests on the floor, a yoga block or the lower leg. This arm supports the weight of the upper body. However, if that arm is lifted then the legs, pelvis and the abs on the uppermost side of the body then have to work against gravity to support the upper body.
They get strengthened in the process.
To gradually improve stability, reach the arms, then lower the arms to suppor the body. Do these actions repeatedly in time with the breath.
Note that with the hands reaching past the head weight is added to the pose making the supporting/stabilizing muscles do more work.
In these case the stability work can be in stabilizing the feet, one or both legs and even the back of the spine.
Lifting the both arms (or in the case of twisting triangle, the one arm) exercises the feet, leg and hips, particularly the buttocks, and also strengthens the spinal erectors, particularly if the spine is straightened or bent backwards. In this case these muscles work against the weight of the body and head.
Extra weight can be added to the Forward Bending Triangle posture to by reaching the arms forwards.
To work more on the back of the legs a pose like Bending Forwards with One Leg Lifted can be useful.
Note that the lifted leg is forwards, beneath the hips, as opposed to reaching back. This shifts the bodies center of gravity forwards, meaning that with respect to the foundation the hips have to move back. And that means more work for the buttocks and hamstrings of the supporting leg as well as the deeper hip muscles like the obturator internus.
An exercise like Standing Knee Lift while balancing on one foot can be used to educate the psoas and other hip flexors. In this case these muscles work against the weight of the leg.
To increase the weight reduce the bend in the knee.
Another exercise to improve stability is based on half moon yoga pose.
This pose can be challenging because the supporting foot is turned out relative to the pelvis. This puts the supporting leg hip near its bony limits. This can affect the ability to control the knee, ankle and foot.
This is a pose where muscles can work against each other as well as against body weight to create stability.
Note that the hip muscles of the lifted leg work against the weight of the leg to keep the leg lifted.
For a greater test of stability try lifting the hand.
One of the ways to visit shoulder stability while standing is to shift weight forwards onto the hands while doing a standing forward bend.
The more you shift forwards the more you have to use the hands to help support the weight of the body. In this case the muscles that move the scapulae relative to the ribcage can be resisting the movements of the ribcage towards the floor.
The arm muscles can be working against each other to stabilize the arms. In general what you should feel as you rock forwards is some change in arm tension and arm effort. Your arms and shoulders will have to turn on in order to support your body.
In a laying down posture like bridge pose where the legs are used to lift the hips, the leg muscles at the back of the legs, particularly the glute max, work against the weight of the pelvis, thighs and the lower part of the upper body to keep the pelvis lifted. The shoulders can also be used to press the ribcage upwards by pressing the shoulder blades down into the floor. The action actually used in this case is shoulder blade retraction.
One way to increase the work load in this stability exericse is to lift one leg. The supporting leg then has to double the work. To work on both hip and waist stability focus on lifting the lifted side of the pelvis also.
In a pose like table top you can use a similiar action, retraction of the shoulder blades, to lift the ribcage higher.
In this pose you can try lifting one arm or one leg in order to practice stabilizing the supporting leg or shoulder. In the case of lifting one arm the challenge can be to keep the supporting side shoulder blade retracted.
In a semi inverted posture like downward facing dog stabilizing effort can again focus on the shoulder blades. In this case you can use the muscles that work between the shoulder blades and ribcage to push the ribcage away from the hands.
The shoulders will move closer to the ears as a result. Or you could focus on widening the bottom tips of the shoulder blades while pulling the inner edges of the shoulder blades away from the head. This supraversion of the shoulder socket may also cause the ribcage to move away from the hands but will also result in the shoulders moving outwards.
In a pose like dog pose you can use the leg muscles to lift the knees by pressing the fronts of the feet into the floor. This same action can be used to lift the knee in a high or low lunge.
You can also use the scapular stabilizers to lift the ribcage relative to the shoulders and keep it lifted so that the serratus anterior muscles are working against the weight of the upper body (and gravity.)
With knees lifted you can lift one hand or one knee to work on the stability of the supporting hand, leg and/or hip.
In a beginners variation of chaturanga dandasana you can gradually increase the stabilizing ability of the arms with elbows bent by lifting only the ribcage (and not the pelvis), then lifting the pelvis and ribcage but not the knees, then by lifting ribcage, pelvis and knees.
A variation of this is to keep the chest on the floor and press the knees down to lift the pelvis then press the feet down to lift the knees.
For more exercises for improving midsection stability see the yoga poses for abs page.