The most common uses for apostrophes are to show possession of objects by nouns and to indicate omitted letters in common contractions. Other uses for apostrophes include indicating omitted numbers, designating plural possessives and forming plurals of lowercase letters. In the phrase, "The cat's toy," the apostrophe is used properly and indicates the toy belongs to the cat. Without the apostrophe, that phrase would read "The toy of the cat."
A common contraction requires the use of an apostrophe to indicate any omitted letters. The most common placement of the apostrophe is prior to the last letter of the second word of the contraction. Some examples include "don't" (do not), "who's" (who is) and "I'm" (I am). Examples that do not strictly follow that rule include "she'll" (she will) and "could've" (could have). Personal pronouns, such as "our," "its," "your" and "whose" never take apostrophes.
To use an apostrophe to indicate plural possessive, place it at the end of the word. In the sentence, "Mr. Jones' house is on the corner," the apostrophe indicates that the house on the corner belongs to Mr. Jones.
Some sites that provide miscellaneous examples of apostrophe usage include Grammarbook.com and OxfordDictionaries.com, as of 2015.