What Happens To A Person When They Die?

There are many physical things, like cremation of the body, burial, etc. But we are all energy and that energy is released. Rest assured, all is fine in the universe.  There is an old poem that I try to remind myself of, as I have lost many close to me, where did you come from baby dear, out of the everywhere into the here.  There is a reason for everthing and that is why I am agnostic, because i believe there are certain truths that are never meant to be known to us.  Pray, and say farewell.

Their soul goes to heaven or to hell based on whether they are born again or not

Soul never die but it transfer this world to here after. Then if this soul has True Faith that Allah is one & Prophet Muhammad is His Last & Final Messenger with good deeds its destination will be Paradise for ever and will have a body & features related to Paradise by the Grace of Allah, and if this soul has no true faith on Allah & on his Prophet its destination will be Hell forever will have a body & features related to HELL as per anger of Allah,  but if soul has True Faith and no good deeds it will get punish in Hell & then enter in Paradise forever and may be forgiven by Allah to enter in Paradise.

Their soul is left with their conscience to think about it and respond to it until judgement day.

As an atheist, here is my practical take:
There is 0% scientific evidence for a "soul" which continues on after death, but there is evidence that everything constituting a living human being either ends immediately at death or soon after, the decay of the body being the longest process of dissolution.  I believe it's game over permanently.

The question here is what happens WHEN a person dies, not AFTER they die. Clinical Death occurs when there is a cessation of all vital functions of the body, including the heartbeat, brain activity (including the brain stem), and breathing.

They remain on this earth until the resurrection.