Most people got the concept of time dilation in space from science fiction films, the most popular one being ‘Interstellar.’ It used the concept of time dilation from the perspectives of general and special relativity. In interstellar, the dilation phenomenon had a greater effect due to the use of extreme variables. For instance, the planets shown were considered to be in proximity to a giant black hole.
In reality, our astronauts are present in an International Space Station which is orbiting the Earth in a low earth orbit. Even if these astronauts go on the moon, they will not face a time dilation that is remotely close to the scenario depicted in the movie. Moreover, such time dilation can not be expected even when the International Space Station orbits around the Sun.
The International Space Station orbits the Earth at 17,500 mph. According to the NASA instructor Robert Frost, the astronauts experience a time dilation of -0.00002646 seconds per day. A crew member would stay on the ISS for about 180 days that accounts for a total time dilation of -0.0047628 seconds. To make a difference of just one second compared to the time on Earth, they would have to stay aboard for almost 140 years.
That being said, the concept of aging is not relevant to the relative time. The rate of aging of the cells remains the same irrespective of the time dilation experienced. Time is altered, the aging process is not. NASA also did another experiment on aging in space, the details of which you can read here
In contrary to the common belief, due to the stress of having to live in space, humans would age faster. The radiation in space could also prematurely age a living being. However, to experience a significant time dilation, a person must be traveling at speed somewhat comparable to that of light.