For more detailed information and examples, please see The Associated Press Stylebook (55th edition). Punctuation is discussed on pages 333-345.
Below are several examples of possession and the apostrophe.
The boy's dog [Singular noun not ending in s takes 's to show possession of dog by one boy]
The boy's dogs [Singular noun not ending in s takes 's to show possession of dogs by one boy]
The measles's rash [Singular noun ending in s takes 's to show possession by measles]
The boys' dog [Plural noun ending in s takes s' to show possession of dog by boys]
The boys' dogs [Plural noun ending in s takes s' to how possession of dogs by boys]
The woman's dog [Singular noun not ending in s takes 's to show possession of dog by one woman]
The women's dog [Plural noun not ending in s takes 's to show possession by women]
Unlike other major styles such as MLA, APA, and Chicago, AP does not use the serial comma.
I like cooking, stamp collecting and videogames. (AP does not take a comma before the conjunction "and" when listing a series of items.)
The most important subjects in the curriculum are science, math, and reading and writing. (AP does take the serial comma when the last element in a series is linked with an "and," as in "reading and writing.")
Non-essential, parenthetical, dependent clauses take surrounding commas. See the Writing Academically Video.
Stacy, for her part, will never study at Panera again. ("For her part" can be removed and retain the meaning of the sentence. And it cannot stand alone. That makes it a non-essential, parenthetical dependent clause.)
Use a comma and a conjunction (and, but, for, etc.) to separate two independent clauses in a single sentence. See the Writing Academically Video.
I was breastfed, but my family members were fed formula. (Two independent clauses joined with a comma and a conjunction.)
Use a comma after a "speaking" verb preceding the exact quotation, but not when the quotation is an incomplete sentence.
She exclaimed, "He's the one!" ("He's the one" is a complete sentence and a direct quotation, so there is a comma before the "speaking" verb.)
She stated that she "saw them steal the car." (The fragment "saw them steal the car is not a complete sentence, so it has no initial capital letter and no comma before it.)
If you must use parentheses, sentence fragments or complete sentences that are part of a sentence do not take a period inside the parentheses. However, if the parenthetical sentence stands alone, it takes an initial capital and an ending period inside the parentheses.
The best video game of 2017 was Horizon Zero Dawn (arguably).
The best video game of 2017 was Horizon Zero Dawn (though others might say Breath of the Wild).
The best video game of 2017 was Horizon Zero Dawn. (Though others might say Breath of the Wild.)