The most common way to form a possessive in English is with apostrophe and s: "a hard day's night." After a plural noun ending in s, put just an apostrophe: "two hours' work" (i.e., "the work of two hours"). If a plural doesn't end in s — children, men, people — plain old apostrophe-s: "children's," "men's," "people's." It's never "mens'" or "childrens'."
There's also the opposite case: when a singular noun ends in s. That's a little trickier. Most style guides prefer s's: James's house. Plain old s-apostrophe (as in James' house) is common in journalism, but most other publishers prefer James's. It's a matter of house style.
Note that, with the exception of the little-used one, the possessives of pronouns never get apostrophes: theirs, not their's; hers, not her's; its, not it's. See It's versus Its.
Apostrophes are sometimes used to make acronyms or other abbreviations plural (another matter of a local house style). My preference: don't use apostrophes to make abbreviations plural — not "They took their SAT's," but "They took their SATs." The only exception is when having no apostrophe might be confusing: "Two As" is ambiguous (it might be read as the word as); make it "Two A's." Never use apostrophes as single quotation marks to set off words or phrases (unless you need a quotation within a quotation). (Lynch)
