How could one determine if two
unidentified organisms share a common
ancestor?

Evolutionists determine that two organisms have a common ancestor is by looking at fossil evidence in different rock layers using the law of Superposition (Oldest layers are on the bottom, newest are on the top) and compare the skulls or other bones to each other in order of oldest to newest (or newest to oldest). Another way to determine this is to examine the amount of DNA a certain species shares with another species. An example of this would be that Humans share roughly 90% of our DNA with chimpanzees or the other Great Apes.

Explanation:

DNA

They can look at the DNA it's the most common one.

There are 4 pieces of evolution and they are

Fossils , Geography , Embryos / DNA , Anatomy

Fossils: Physical remains of species , Determine age, location,  environment

Deeper layers = older

Geography: Proves species share common  ancestors, depending on where

they live

DNA: BEST evidence because it’s the  MOST ACCURATE

Similarities in the early stages of  development

Similarities in DNA

More similarities = closely related

More differences = not related

Anatomy: Compare body parts of different  species to see how they evolved

3 different structures:

Homologous (same structure,  different function)

Analogous (similar structure,  different organisms)

Vestigial (body parts that no  longer serve a purpose)

All of that are in evolution

Hope it helped! ( Gave u my biology notes :D)

answer; /// i do believe its (heredity); good luck