Helping "old" people really needs expanded on. How old - and how limited are we talking about? When I retired from the Post Office I was asked to do maintenance at a Senior Center with ages from around 60 to close to 100. There is training someone in preparation for getting older who is still highly trainable and then there is training someone who "is" older and the common training ideas are way too serious for these people - regardless of actual years on earth age. One of the problems is that many of the people coming up with "how to train the elderly" aren't elderly enough themselves and have no concept of the limitations and issues the elderly face. Oh sure - you can take the average 50 year old and do all kinds of things with them and this will certainly help them as they age further - but try that with someone who is 75 already and you can easily do some serious harm to them - depending on the individual of course. The average trainer in a gym today doesn't have the ability to train a 25 year old without harm - and the things they try with the actual elderly are criminal. If I was forced to pick one thing for the actual elderly to do (and of course we aren't forced to do that) - I'd choose something like Tai Chi - at least in the beginning. But judging from what was an admittedly very small population where I worked - they liked dancing more than anything else I could show them. All these wonderful training ideas kind of fall apart when the person is unable to get out of their chair without help - there is old and then there is old - two different things entirely. One of the biggest problems in training the truly elderly is getting them to a facility where the things I Love Big Chicks talks about are possible equipment wise. For example the place where I worked had no training facility at all and many ladies in their 80s and 90s also couldn't drive - so what we had was a "commons" area with zero equipment to work with. The social aspect of group training also encouraged many who otherwise wouldn't even try.
Old is entirely as relative term. That's why, above, I mentioned "frail". Some older people, 40 and up, usually 50 and up, have no concept of heavy, of moving well, of doing anything with their bodies at all, and, like Climber511 says, they can't get up out of a chair. I always evaluate the folks I'll train based on their ability to do normal, everyday tasks- and then see where I go from there.
The things I consider are:
Ability to walk 1/4 mile or so on a sidewalk
The ability to get up and sit down repeatedly (three times in a row)
how rounded their backs are (rounding between the shoulder blades)
how bad their pelvic tilt is and whether it's anterior or posterior.
I also need notes from their Doctor about what they can and cannot do. I spend most of my training time with older folks trying to correct years of horrible posture. And again, I say older because I don't know whether older is 45 or 80; it's more a factor of detrained/untrained.
I will say that swimming doesn't keep these old folks in shape at all. I go to the Y once or twice a week with my daughter and all the older folks who swim, even for 30 minutes or more at a stretch, look like hell. Bad posture, fat, hardly any muscle tone at all.
But dancing is pretty popular for the older people, and dancing, moving, maybe some basic bodyweight stuff is great. Do push-ups on a wall, just use a chair to sit up and get down, etc.