An apostrophe is used:

a.    To show possession

Following a noun: an apostrophe plus an s.

e.g. The book’s cover.

But—following a noun that ends in s: an apostrophe only.

e.g. The puppies’ tails.

Exception—personal names that end in s add an apostrophe and an s.
(But—Japan Harvest adds only an apostrophe to the names Jesus and Moses.)

e.g. Jones’s; Keats’s; Jesus’; Moses’

Note: Possessive pronouns—including “its”—already show belonging, so do not need an apostrophe. (“Its”—it is—indicates omission.)

b.     To show omission

e.g. the ’70s, don’t, can’t, I’ll, it’s.

c.     To form a plural with lowercase letters (but not numerals or uppercase letters)

e.g. x’s and y’s, but 3s and PhDs. 

d.     (Rarely) In a proper geographic name

e.g. Pikes Peak, but Martha’s Vineyard. 

With only a few exceptions in the US and Australia, “apostrophes suggesting possession or association are not to be used within the body of a proper geographic name”¹. Perhaps more commonly used in Canada and Britain, the apostrophe usage debate continues to rage. Check an official map or article for proper spelling.

¹Principles, Policies, and Procedures for Domestic Geographic Names, p. 41