How do the clues at a crime scene of a mysterious death investigators determine what might have occurred and identify or exonerate potential suspects?

Well if there was a murder weapon there at the death scene, the investigators check the weapon for fingerprints. Same for if there are random murder objects lying around anywhere, they'd check it for fingerprints. I suppose after checking the weapon or murder object, they set it under a scanner that is connected to a computer and it tracks who's fingerprints were last on the murder object and the title and picture of that person comes up.
Hope this helped.

Nail fungus, which can cause the nails to crack, peel and change color and texture.