To begin with, you have to drop all contractions but spell out words in full, smile less and talk gravely, almost academically. And then you should never raise your voice when speaking. Instead of saying, "Man, I had a ball at Mr. Montgomery's party yesterday!" you say, "I have yesterday experienced enjoyment at Mr. Montgomery's informal gathering" in a low, matter-of-fact tone of voice. By the time you get the hang of it you'll probably and eventually reach a point where you'll downplay every other sentence into stricter observance and unshakably turn your back at anyone who attempts to speak informally with you.
I think Henry Cunha, a native speaker of English himself, may provide more examples of formal speech.