There are two approaches how it can be done.
It is clear that aging is the accumulation of damage in our cells and body, being embodied by what we call age-related diseases. One approach is to fight these symptoms of aging we all are familiar with. There are seven variables that lead to aging and there is research going on into every one of them right now (some more than others).
Once we can fix all seven of these things, we are done abolishing physical aging. With this approach it will be necessary to periodically remove these accumulated damages from our bodies, but that will be a small price to pay for near-immortality.
Those symptoms of aging have all one common root cause, an inefficient cell-maintenance (homeostasis).
There is strong evidence that aging and longevity are controlled by a multiplicity of molecular and cellular signaling events
that interface with environmental factors to maintain cellular homeostasis. A decline of our cells capacity to keep high-efficient homeostasis
leads to dysfunction of specific cell types and tissues, rendering the organism susceptible to a range of chronic diseases.
Such decline is only possible through an intrinsic over-time alteration of our gene-expression.
The only way to stop this from happening is, to determine which specific genes are involved in this process,
so that their expression-setting can be reprogrammed, ultimately making you stay and look young without a time-limit.
This method would require the least maintenance with maybe only even a one time treatment, but this is the high-end method and there will be probably others before
Like any technology, when it first starts off, it will be a bit shaky, a bit risky, it will be very laborious and expensive, but there will be enormous market pressures that will result in progressive refinement and improvement to the technology so that it becomes more effective and convenient.
Potentially forever, however, if you had never seen any mortality statistics, you might subscribe to what's called the "lightning bolt theory" of mortality.
In this view, death is the result of a sudden and unexpected event over which you have no control. It's sort of an ancient Greek perspective:
there are angry gods carousing carelessly overhead, and every so often they hurl a lightning bolt towards Earth,
which kills you if you happen to be in the wrong place at the wrong time. These are the "lightning bolts" of disease and cancer and car accidents,
things that you can escape for a long time if you're lucky but will eventually catch up to you.
Your probability of dying during a given year would be constant, and wouldn't increase from one year to the next.
From current statistics this probability for the populations of the UK and USA is somewhere around 0,05% per year (varying on location and lifestyle)
Taking it to numbers with such mortality rate, out of 1 million people today, 950'000 would still be alive after 100 years,
780'000 after 500 years and around 600'000 in 1000 years. And then after ten thousand years - if you are lucky - you will be one of the 7000 people still alive.
This is also a great argument for people who falsely fear that immortality will lead to overpopulation. As if all 7,6 billion people who life today would become immortal, after 18'000 years only 1 million of them would be still alive.