Scapular stabilization can be one of the first steps in improving arm strength in arm strengthening exercises.
The first step towards improving (or learning) scapular stabilization is developing scapular awareness. That basically involves moving your shoulder blades while the arms aren't supporting weight as described in scapular awareness.
Five basic positions for scapular stabilization, which involves stabilizing the scapula while the arms are bearing body weight, include:
Variations of these positions include bending the elbows and placing the forearms on the floor.
Because I start a lot of my yoga classes on the floor, in seated positions, table top is often one of my first scapular stabilization exercises.
I often start with easy table top, with the hips on the floor.
In easy table top the scapular stabilization exercise can be to move the shoulders back first, retraction, and then press them down. Since the hands are on the floor this then causes the chest to lift relative to the shoulders.
To improve awareness and control the initial exercise isn't to hold this position but to relax and repeat the action. And rather than just relaxing and repeating x number of times, the idea is to do it while focusing on feeling the shoulder blades and/or chest.
After a rest (I often do boat pose variations as a way to rest the shoulders) the next exercise can be to do table top with hips lifted, either slightly or fully, and then keep them lifted while using the shoulders to lift the chest and then lower it.
If I have new students who lack shoulder awareness then I'll start with basic scapular awareness exercises (retracting and/or protracting the shoulder blades) while the arms aren't bearing body weight.
I also like to do this exercise with the fingers pointing forwards and then with the fingers pointing backwards (not shown).
Another scapular stabilization exercise I like to do from the sitting position is "lifting up".
For this start with the hands beside your hips. Either protract and then press the hands down and then lift the hips or retract and then press the shoulders down and lift the hips.
I like to teach and practice both combinations. I may just have my students press down and then lift the hips.
In all cases, a key action is pressing the shoulders (and hands) down first. Then lifting the hips.
While sitting on the floor, another possibility for Scapular Stability is side plank.
With knees bent and hips and knees on the floor, you can practice pushing your ribcage up and inwards, away from your hand.
Some people find this problematic and bend their elbow as a way of getting their chest closer to the floor. Basically you can use protraction to lift the ribcage and relaxed retraction to let it sink back down. Here again I'll often return to simple shoulder awareness, have them practice moving the shoulder with the hand free.
You may find it easier to do with the hand further to the side.
Generally I'll have my students practice lifting and lowering their chest. Then I'll have them lift their hips while keeping the scapula protracted. This can be don with knees bent initially, then with either the top or bottom knee straight (top or bottom foot pressing the floor to lift the hips).
Because this only uses one arm, I like to switch arms frequently so that each arm stays fresh.
My general starting point for scapular stabilization in plank type poses (not side plank but belly facing down plank) is cat pose. Here the first exercise is to protract the shoulder blades to lift the chest away from the floor and then relax and repeat.
To add weight try first protracting and then lift the knees an inch off of the floor (press the feet into the floor to do so).
To work towards full plank start with one leg straight and the other knee on the floor. Protract, then press the straight leg foot down into the floor. Then lift the bent knee.
Another option, particularly if your lower back feels uncomfortable, is to pull inwards on the belly, then protract, then push the straight leg foot down and lift the knee.
Scapular stabilization can be tricky in downward dog.
The trick is learning to feel the shoulder blade(s) lifting with the arm(s) over head. Then try to get the same feeling in downward dog with knees on the floor.
In this case use the scapular stabilizers to push the ribcage back away from the hands, then relax and repeat.
From here try the same exercise with knees lifted but bent.
For more of a challenge, start with the knees on the floor, push the hands forwards against the floor, then lift the knees. Finally try it with the knees straight. In this case start with knees bent. Push your chest back and then straighten the knees. Additionally lift the heels after straightening the knees or push the heels down.