If someone dies while they're sleeping, how will they realize that they're dead?

It depends on the individual.  Some people do not even realize they are dead when they die while awake, so its hard to say that everyone will even be able to make that realization immediately or without help.  

If I were to die while sleeping, I am pretty sure I would be aware of what happened.  There are physical and psychological triggers which bring our consciousness back to our bodies while we are sleeping, and I am pretty sure physical death would trigger our consciousness back to our bodies during the moments of death.  

If this did not occur, the knowledge of my death would most likely be directly experienced while in the dream state, and rather than coming back to my body and then phasing into higher nonphysical realms, I would go from whichever nonphysical realm I was in during sleep directly to my nonphysical afterlife destination.  

Also, InvenTech,

You and the people here are very interested in the afterlife, so I expect we are all aware that these different states of consciousness are important. You would notice the differences--that in the afterlife you move through 'space' and physical matter differently,  the incredible light, etc.
I suspect the souls who are unaware of their transition to the afterlife are rather unaware of many aspects of their lives.
You will not have that problem.  :)

Bets