PUSH UP: Do not lower further than 90 degree elbow bend. Keep arms in at side and shoulder blades down (not shrugged) to protect shoulder. HOLD down position 5 seconds. Repeat 10 times. Begin from knees. Progress to feet. Then increase to 2-3 sets as tolerated.
UNWEIGHTED PULL UP: Choose bar height that allows you to pull up with good FORM. Hold up position for 5 seconds and SLOWLY lower. Don't lower into locked elbow position or full shoulder stretched position, but rather to a very slight bend still in the elbow and "active" shoulder muscles to protect these joints. Do 10 reps. Add 2-3 sets as tolerated.

NEGATIVE PULL UPS: This is similar to the unweighted pull up, but utilizes eccentric contraction which is safer for beginners or those with shoulder injuries. To get into the start position, a chair or bench is needed (not pictured). From the start position, VERY SLOWLY lower into the end position, again being careful not to hang passively from the shoulder joints (keep shoulder blade muscles active and elbows slightly bent). The photo does not depict this well. Do 5-10 reps and taking 4-6 seconds for each lower. Practice with varying grips (palms forward, backward, neutral) if the option is available. Progress with reps until your strength improves. Every few weeks, attempt a concentric pull up (regular going up), but only after a good warm up. Once you can perform 1-2 regular pull-ups, these can be added to the routine.

HANGS: Keep shoulder blade muscles active! Do not fully extend or hyperextend elbows. Hang 6-10 seconds. Repeat 6 reps. Progress with HOLD time as you improve. Practice with varying grips (palms forward, backward, neutral) if the option is available.
SQUAT WITH OVERHEAD PRESS: Slowly lower into squat, then explosively press upward out of squat while pressing arms overhead. Begin with light weight. Progress as tolerated. 10-15 reps. Lowering phase should take 4-6 seconds. FORM!