INCORRECT: The doctors daughter broke her nail.
CORRECT: The doctor's daughter broke her nail.
In this example, we're only referring to one doctor, which makes the subject singular. (I'll explain more about singulars and plurals in the next example.) An apostrophe must be used to separate the "s" in "doctors" because it describes possession.
INCORRECT: The workers meals were already made for them.
CORRECT: The workers' meals were already made for them.
In this case, there is more than one worker we are referring to, which means the apostrophe comes after the "s" to clarify that the meals belong to the group.
INCORRECT: The cat's were hanging upside down from the trees.
CORRECT: The cats were hanging upside down from the trees.
An apostrophe is not used in this scenario because there is no indication of possession.
INCORRECT: Its a wonderful day in the neighborhood.
CORRECT: It's a wonderful day in the neighborhood.
The "it's" needs an apostrophe in this case because the word is a shortened form of "it is."
INCORRECT: The dog wagged it's tail.
CORRECT: The dog wagged its tail.
In this example, the "its" shows possession and is not a shortened form of "it is," so an apostrophe shouldn't be included.