Omission of letters
The apostrophe indicates when a letter or letters have been omitted from a word. This happens most commonly with contractions, or the shortening of two or more words into one word. Do not becomes don't, we are becomes we're, etc.
Letters can also be omitted from a word when the writer is attempting to convey an accent. The most common example of this is when a character with a Southern or Western American accent leaves "Gs" off of the end of a word, i.e. runnin' or somethin'. This can be tiresome and difficult to read, however, so do it sparingly.
Apostrophes are also used to create possessives. You know the drill, I’m sure. You add an apostrophe and an S (‘s) to the end of the word to indicate that the word is now being used to imply possession. Brad’s badge and his wife’s sweater.
Note: even if a word ends in s, you still add an ‘s to the end to create a possessive, if the word is singular. Chris’s computer and the actress’s costume. If the word has an s on the end because it is plural, then you only add an apostrophe to denote possession. The Johnsons’ house or the babies' laughs.
You do not use an apostrophe to create a plural. Not ever. (This was done in certain cases in the past, but has largely fallen out of use nowadays. Some people still cling to it, but you don't need to.)
It's is a contraction meaning it is. This is the one place where a possessive does not use an apostrophe: its means "belonging to it." Don't mix them up.
Do not use an apostrophe with a verb. Not ever. Wrong: She love's me. Right: She loves me.