TLDNR (as the kids say): 2-3 sets of 10-15 reps, bicep curls, overhead press, hip hinge/dead lift, overhead triceps press, squats.
Long version with more detail:
I use this routine with 12 or 20 pound dumbbells as a warm-up before a workout, short movement session on “rest” days, after a run, to calm my nervous system, mobilize the fascia on the posterior/back side of my body. You should start lighter if these moves are unfamiliar or you're new to the BOSU. I’ve been doing this little routine consistently since PT school in the early 2000s. The feedback from the weights and instability of the BOSU helps keep my pieces working together very nicely. I sleep better and have minimal to no joint pain when I do this about 2 times per week. It's definitely noticeable on weeks that I skip it. No guarantees for the same results for everyone.
This series can be performed standing with feet on the floor or on an unstable surface (BOSU, balance disc, etc). The bicep curls and overhead press can be performed on two feet or standing on one foot. The overhead triceps is a little dicey on one leg. You don’t want to whack yourself in the head with the weights. Might want to practice a few times on two feet solid surface with the following cues before adding the balance component.
Bicep curls: seems simple enough, hold the weights at your hips, palms facing forward, bend your elbow and straighten your elbow. Many times people with shrug shoulders up to ears with this one especially as the weight increases. To avoid wearing your shoulder blades as earrings, reach your elbows to the floor when you bend them. Mobilizes/reeducates upper traps
Overhead press: again can be a very simple motion, but often there is popping, grinding, pinching with loaded overhead motion at the shoulder with this one. Elbows at shoulder height reaching mostly out to the side, but not straight out to the side, palms facing forward. Press the weight overhead until elbows are straight and weights above shoulders. To avoid shrugging the shoulders with this one as well, press shoulder blades to the floor/pelvis as the elbows straighten. When lowering the weights to start position, reach elbows away from the body. These cues help engage the rotator cuff muscles appropriately and create space in the shoulder joint to avoid pinching/clicking. You can play with the path your elbow takes, try a little more forward or out to the side and see which feels/sounds better. My left elbow will click if it’s too far out to the side. Check in the with rib cage, it has a tendency to over flare with overhead activities (see triceps exercise for cues to manage that).
Mobilizes shoulder joint/reeducates shoulder joint
Hip hinge/dead lift/RDLs/good mornings: this move had multiple names. Hold weights near front of hips/thighs, hinge at the hips to lower weights towards the floor. How far? Short answer: somewhere between knees and ankles. Really it depends, depends on how long/short your hamstrings are and how well you can stabilize low back/pelvis. Ideally you would maintain a neutral position of that low back/pelvis without rounding/flattening or overextending. Your spine should stay somewhere in the middleish of that range by opening up the sitz bones and allowing the femur heads (top of the thigh bone) to sink in the acetabulum (hip socket). Careful when on the BOSU, this one will kick you off balance pretty easily.
Mobilizes hamstrings and hips
Overhead triceps press: take a dumbbell in each hand or a heavier dumbbell between both hands, straighten elbows to reach weight overhead. Check in with lower rib cage/low back (breathe into low back, exhale pull ribs together in front). Attempt to keep rib cage and low back stable while bending elbows reaching weight behind head. Pro tip: use exhale to manage rib cage and reach elbows to ceiling as bend them.
Mobilizes lats and triceps/reeducates stability at rib cage and pelvis
Squats: hold weight at sides/hips, bend hips and knees and ankles to lower weights to the floor. Ideally low back stays in middleish ROM (not too much arch and not too much rounding…..extension/flexion). Your knees are allowed to translate forward over toes a bit. Your knees will not explode.
Mobilizes hips, knees, ankles, low back
I could go on and on regarding cues for squats. Let’s start there, this post has already dragged on longer than it should. I recommend checking Squat University on instagram (@squat_university) or YouTube for more squat info.
Check out Chris Hemsworth using the BOSU:
And here's Chase Daniel on the BOSU as well