I personally think that first, we have to get to a point where we understand what is aging and what causes it. We are quite far from it: as of now, we have lots of "fragmented" knowledge, but there's little unifying that knowledge into a single theory that can explain aging from when we are born until we die. If, and when we possess that knowledge, we will then need to have tools to address those mechanisms. This is far from trivial: think of cancer, for example. We have so much knowledge and we understand almost entirely why it happens, but we don't have good enough tools to go and fix those underlying causes and mechanisms the majority of the time. Here, there is little that the general population can do, other than actively advocating for more research and more funding.
However, what society as a whole can, and should do, is discuss the implications of immortality. Not only for the individual, but for society itself. Let's say that we now manage to make everyone stop aging.
- What happens to older people who can no longer monetarily contribute to society and need constant support from those around them? Today, the "social contract" determined that current taxpayers support previous taxpayers until they die. What happens if the previous taxpayers do not naturally die?
- If we don't die to old age, it will become apparent very fast that we have to stop reproducing, or we will quickly overcrowd the planet. How do you prevent (morally and legally) everyone from reproducing? Who will get to reproduce to replace the smaller number of humans who died to accidents? Who decides it?
- By preventing people from reproducing normally, it is almost as if we are preventing other humans from being born. In other words, in an "immortal world" with population control, while you remain alive, no other people can "take your place" for as long as you decide to remain alive. Is this morally acceptable?
- What happens to those who simply get bored of living? Should they be allowed to end their own lives?
- Should "younger" people have to work forever?
Of course if we get to a stage that we manage to colonize other planets and we're not limited to Earth, we could just send "immortal humans" to those planets. But what if that's not the case? At the moment, it seems to me that we are not prepared for immortality.