By aerobics I mean any exercise that raises your pulse into the training range and keep it there for 15-20 minutes. Bodybuilders usually call this cardio, rather than aerobics.
The exercise itself can be just about anything that makes you sweat. 30 years ago I was a runner, and running is still one of the most efficient aerobic fitness regimes. But a foot injury and the prospect of other joint injuries ruled out running for me. Stationary bikes and steppers like StairMaster and Precor machines seem to work fairly well, except I find them boring, and it turns out that fast walking is more interesting.
Before anyone undertakes any strenuous exercise program, they should of course get medical advice. When I was 50 I had an exercise electrocardiogram, which is a gruelling test to make sure your heart can stand it. I decided I was never going to do that again, however, because basically you run on a treadmill until you drop -- the last 10-15 seconds are total hell. But it's the about only way to be reasonably sure you won't kill yourself by working out. Since I know I have a good heart, clean arteries, and a good family history with respect to heart disease, I decided to get on the stepper without further medical advice, being very cautious and very careful in the way I approached the workouts. Since I switched to walking for cardio purposes, I've found a heart-rate monitor to be very useful for not overdoing it.
A conservative max rate for a 60-year-old would be 128, so that's what I used as a guideline. My conditioning and confidence have increased, so I now use a max of 140, with occasional short bursts above that.
When I first started out, I did the cardio first, before any weight lifting I was going to do that day. I've since learned that it's better to do cardio after weight training if you're doing both in the same workout session.