"I should of looked at that earlier."
"I would of bought it, but I had to pay the water bill."
"I could of gone to the game, but I was too tired."
"I may of put the book in the bedroom."
Contractions include such words as can't (cannot), won't (will not), shouldn't (should not), didn't (did not), I'm (I am), we're (we are), and ya'll (Southern for "you all").
In the above cases, the words should, would, could, and may are joined with the word have, which makes much more sense than using a preposition. Oh wait, I forgot--the term "preposition" might be foreign to some of you:
So, what did we learn today? We learned that of is a preposition, and have is not. We learned that contractions really do exist, and they exist for a reason. Though seemingly tricksy for some people, most contractions are easy to reason out (except for ain't which, while it is listed in the dictionary, is not really a word since there is no such thing as "ai not").
So, to recap:
*Should've, would've, could've, may've, and you're (you are) welcome.