We can start with a simple rule for apostrophe use from my colleague, Carole Marquis: use 's for all cases of possession except when the word is a plural with s. When the word is plural and ends in s add an apostrophe after the s.
To expand on it with a few examples to see how it works, here are some sentences.
Doug's car is parked on the street. (singular subject)
Doug's cars are parked on the street. (singular subject with one possessor)
James's car is beside Doug's. (singular subject with one possessor that ends in s)
The children's helmets are on the shelf. (plural subject with plural possessor formed without an s)
The boys' helmets are on the shelf. (plural subject with more than one possessor)
There are a couple of cases where the rule needs expansion. In a compound construction, the apostrophe is used appropriately with the final word in the compound.
Carlos and Juan's bikes are in the repair shop. (Two or more possessors in a series)
My brother-in-law's phone was stolen. (singular compound noun possessor.)
When we use a possessive noun, that is, when we use an apostrophe to signal possession, the noun acts like an adjective in most sentence constructions.
The blue car is parked on the street.
Doug's car is parked on the street.
The noun is car and the word modifying or limiting its meaning in the first sentence is new. When we use the possessive in the second sentence, it serves a similar purpose of modifying or limiting the meaning of the noun. In the second sentence, the noun is limited to a car belonging to Doug.
Knowing that possessives precede a noun tells the writer to anticipate possession when a person's name or family name is in front of a noun. This helps in determining whether or not to use an apostrophe in some sentences.
Test clue: Adjectives are not plural in English, so most adjectives do not have an s at the end of the word. If you have a sentence on a test and the word before the noun has an s at the end of it, it will often be possessive, either singular or plural.
Adding a little confusion
This is all well and good, but what about this sentence?
The Ford car is parked on the street.
Ford is a family name, the family name of the Ford car manufacturing company's founder, Henry Ford. Ford is the car's brand name.
The Ford's car is parked on the street,
In this sentence, the apostrophe tells the reader that the car belongs to a family named Ford. If the car was a Ford, then it would read.
The Ford's Ford car is parked on the street.
Or more likely
The Ford's Ford is parked on the street.