If there is nothing after death how do we find out?

[Angrboda]

This is not necessarily true. While I would agree that it's improbable that there is a naturally occurring process which would "takeover" the hosting of our mind after the death of the physical, it's not impossible in principle.

Let's say it is possible. Where is the evidence that the possible is also the reality in the particular case of the person in question?

You're probably asking the wrong person, as I don't believe it occurs, so I'm highly skeptical of evidence presented in favor of the hypothesis. However I do know that people who do believe in the hypothesis, as something to be explained scientifically, typically bring up near death experiences, OOBE, and past lives studies. (A book from a skeptic, Mary Roach, on the subject of life after death and such evidences, Spook, likely goes into the subject, but I fell ill the day I had planned to read it, so can offer no specifics.) I know that there are a few well known researchers in the NDE and past lives field, but I don't remember their names offhand. I can look into recovering that info if you like, but I rather suspect you weren't interested in the specifics. If you are, let me know and I'll see what I can uncover.

Oh, and this just occurred to me, but I'm not going to research the details. There once was a gentleman who had prepared a special bed which was attached to a precise scale, and he would put dogs in the contraption and observe their passing. According to his experiments, the dogs lost a slight bit of weight at their passing. I believe he inferred that this lost weight was the soul escaping at death, but I might be misremembering it. There are also many people who believe that their experiences under psychotropic substances gives them insights into the nature of time, existence and the after-life, but that's also pretty unimpressive. (Though listening to people prattle on about their experiences with DMT does have some modest entertainment value.)