Leave apostrophes out of plural words. This is perhaps the most common apostrophe error. "I bought apple's at the market," is incorrect. It should be, "I bought apples at the market."
Do use an apostrophe when the plural is of a single lowercase letter, as in, "I crossed my t's and dotted my i's."
Choose a consistent style when there is no clear right or wrong. The style guides disagree on whether apostrophes should be used for the plurals of abbreviations or acronyms using capital letters, such as CD or PhD. It seems to be a matter of your preferred style, though know that these days most publications leave out the apostrophe (CDs, PhDs).
Use apostrophes to indicate possession. "Janet's dress is blue." For a plural possessive, add the apostrophe at the end: "The girls' dresses are blue."
Skip the apostrophe for "its" and possessive pronouns. The possessive form of "its" does not have an apostrophe: "The CD came in its own box." The only time an apostrophe is correct in "it's" is when it's replaces "it is," "it has" or "it was," such as, "It's too late to go to the movies." Likewise, you would not add an apostrophe to "yours," "hers" or other possessive pronouns.
Use apostrophes to replace missing letters. Contractions, where words are shortened by removing letters, substitute apostrophes for the missing letters. In "I can't go to the movies," can't is the shortened form of cannot.