Insert an apostrophe followed by the letter S to indicate possession: That was Barry's idea. Use the same system in cases of multiple relationships: That idea came from Barry's mother's next-door-neighbor. This applies to situations involving people (Barry's idea), organizations (the commission's proposal) and corporate entities (GMC's innovation). A good guide to using apostrophes in this situation is to write them the way you say them.
Use an apostrophe without the letter S when the possessor's name ends in S: That was Jules' idea. What you say and what you write differs in these instances You would likely say "Jules's, but you write it without the extra S. Use the same strategy if a possessive noun is a plural: The commissioners' proposal. Remember that the S indicates possession and does not make a plural of a possessive noun. Therefore, you would write children's activities rather than childrens' activities. Children is already a plural noun and does not need the letter S. Add the apostrophe and the letter S to denote possession.
Some words indicate possession without added apostrophes, i.e., mine, his, hers, ours, yours, theirs and its. These possessive adjectives function independently: That was his idea; the next turn is yours; its major components. The most troublesome is "its." We are so accustomed to the contracted form of "it is" (it's) that it is easy to wonder whether we need an apostrophe every time we use "its." Here the rule is strict. When "its" is used as a possessive, there is no apostrophe: its function, its major components, its handle. The apostrophe is used only when we are shortening "it is" to a contraction. It's a cold day, It's time to go, let me know when it's over.
Apostrophes serve as substitutes for letters in some frequently used words and expressions. They let us leave the I out of is: It's a cold day. This and its negative counterpart are the most frequent uses of apostrophes as letter substitutes, what we call contractions: It isn't a cold day. Here the apostrophe stands in for the O in not. Most negative contractions use the apostrophe to remove the O, but a couple go farther. In "can't," the apostrophe stands for the O in not and the second N. Can not becomes can't. In "won't" the substitution involves a spelling change as well. Will not becomes won't. There's a lot of history in this change. What's important for apostrophe users is that the apostrophe contracts the not part of the word. Not becomes n't.
Probably as a design decision to set off brand names, advertisers have confused readers by adding apostrophes to their advertisements. The world will move faster when drivers own 'Vette's.
While technically an apostrophe can be used to show that part of a word is missing (the Cor part of Corvette), this is not common usage. If it were, many people who use part of their name as a nickname would be learning to add apostrophes as early as they could hold a crayon. Setting off the name Vette with an apostrophe rather than writing Vettes is just that--setting it off. Apostrophes are meant to make things clearer, not garnish a word like pieces of parsley. Punctuation needs to mark words, not decorate them. If you can't find a good reason to use an apostrophe, you probably don't need one.