It's all in the wrist. Most young guitarists start off and use their whole forearm to strum; the trick is to rest the side of your hand (from where your wrist is, all the way up to where your pinky starts) just a little bit away from where the strings come off of your bridge (the little metal piece down at the bottom by the pickups). You rest that area of your hand across the strings you're hitting and then use your wrist to pivot your hand for the strumming. It's a little tricky but once you get it down it adds a big new dimension to your playing.