From Personal Experience
I am 86 and in the last year have fallen twice. Fortunately, I didn't break anything. But being put back on my feet by a passerby is not the greatest thing in the world. I decided that I was not going to fall again unless I was hit by a truck. So I started off slowly - only one or two movements of each form of non-stress exercise and building each day until I got to the point that I could run (that's a bit of an exaggeration - but not much) up the stairs, and I'm so stable on my feet that falling is a thing of the past. This can be done in a relatively short period of time - weeks not months.
Do these exercises lying on the bed or standing holding on to a door or window jamb, or something absolutely stable.

The floor is not for me. What I can do standing up or on the bed will get me off the floor if I ever find myself there.
Do exercises in bed, and at another time standing, OR one day bed - next day standing. I do exercises 4 or 5 days a week.

Principally:
1. Never do any exercise without drinking before
2. At any time, if a voice within you says stop, STOP!
3. Very Important: hand grip exercise
Hand grip strength is super important. One suggestion: using a water spray bottle, spray plants, windows, anything except your cat - she will never trust you again.
4. Disclaimer
I have trained only myself. This was not developed to build visible muscle but to facilitate movement and exercise the right to stay upright and off the ground. If you are under the care of a physician, it is advised that you consult. It is gradual development, and although non-stress, it does assume a basic level of movement prior to initiation. It assumes certain movement in or around your living space which can be achieved by following the same pattern of gradual development. The intent is critical.

Not more than 10 minutes. At first it might be only 1 minute - it's amazing how many movements you can do comfortably in 1 minute.
I don't care how young or old you are, YOU ARE NOT IN A MARATHON, YOU ARE IN A RACE FOR LIFE AND GIVING YOURSELF MORE TIME - so rest - It's not how much you can do in 10 minutes, it's how much you can do comfortably - rest between each exercise and even between each movement.
Principles:
- One, never exercise on empty.
- Two, always do exercises slowly. Speed may not get you there safely.
- Three, always do only as many as absolutely comfortable. You are not in the ring fighting for a title.
Completing only 5 of 10 exercises in one session is better than none.
- If you are ever out of breath from or during an exercise, stop and rest until you are breathing normally and your heart rate is basically normal.

In my opinion, if you can get to the point of being able to do 5 minutes of the JustDance Light...by Paula Bickford routine free of support, you have added 5 years to your life. Beware of trucks.

Some exercises on the bed:
If you don't understand one of the exercises, make up your own.
If you don't do some one day, you'll do them the next.
If you feel a cramp, you probably need more water.
  -  move feet in a circle with heels ON the bed, not hanging over the side
  -  toes crucial for balance - squeeze/flex toes up and down and then spread toes apart
  -  without moving feet flex up towards chin and down towards the wall
  -  boxing in air clench/open fists at crest of movement each time
  -  straight arms with hands clasped, swing from above head down to waist, and back
  -  each knee separately, up towards chin and down flat
,  -  lift each leg straight up to ceiling and back down
  -  arms right angle to body on the two sides, lift each arm up and over until roll over onto sides
The following 2 exercises are only done at the end when fully warmed up
  -  arms stretched out to side, do full circle left to right from each shoulder - pass over waist and above head like a windmill. Then do it in reverse
  -  after a rest or some other simple exercise, do the same with each leg separately. Then do it in reverse. Note: I generally do not do arms and legs one-right-after another
finally
  -  sitting on edge of bed, lie back and sit up - only as many times as is truly comfortable
- note: I have apnea, and if I sleep on my back, my tongue falls back into my throat and I suffocate, or saliva falls into the windpipe and I wake up coughing. Have learned to sleep only on my sides, never on the back. So, if I feel that I am falling asleep in the middle of the exercise or at the end, I immediately get over on my side, or get up. Long story short, I was denied insurance for a breathing machine, so adopted the above. This is not medical advice for you, but a warning. Lying on the back can be very restful. See disclaimer below.

Some exercises standing
Again, if you don't understand one of the exercises, make up your own. Holding onto door/window jamb - usually done with fingers only unless you can actually grab on - toes touching wall or jamb - push offs and pull ups
- feet at arms length from wall - arm pushups
- holding on to jamb, slight knee bends for warmup - not too far down
- moving knees together in a circle - left and then right
- toe flex to strengthen balance
- leg pushups until eventually actually squatting down just above feet

Free standing or holding on - step front and back as far as comfortable
- step sideways left and right
- flex toes up
- spread toes
- lift heals up so standing on front of feet

Free standing
- for any free standing, use back of chair as partial support or near to you until really stable
- feet stable, arm and leg swings so upper torso turns to right and left
- arms straight or bent, raise above head, then bend down at the waist and move arms up behind back
- run your hands down legs as far as comfortable - ultimately touch toes multiple times. Picking something up you have dropped could possibly be life saving

Note: balancing on one leg not necessary. Comes naturally from other exercises.

To your health and well being!
Morgan