Cut up the sleeve seam, and this is what you get- a raglan sleeve!
You'll probably want to mark the sleeve, but if you don't and you forget, the longer of the two pointy bits at top goes in back, and the shorter end in front.
Don't throw the rest of the t-shirt way, either. Cut up the sides of the t-shirt, because you're going to need those front and back pieces as patterns, too. You CAN NOT attach a raglan sleeve to a shirt that is supposed to have standard (set-in) sleeves.
To attach the sleeve, sew the sleeve seam up (the one you just cut open), and the sides of the t-shirt. Line up the Longer Point with the back of the shirt, the sleeve seam with the side seam of the t-shirt, and the Short Point with the front, and sew! They're really easy!