How you hold and use your DSLR can make a big difference to the quality of your imagery. Just follow these straight-forward tips, and chances are good you'll improve your photos dramatically.
Use the camera's neck strap. This is more of a safety tip than anything else, because keeping your expensive camera firmly attached to your body by a neck strap will discourage any would-be thieves from running off with it. Additionally, if you are unlucky enough to stumble, a neck strap will stop your camera from flying out of your hands.
Hold your camera and lens. Use your right hand to grip the camera (most DSLRs have a hand grip on their right-hand side), and cup the lens with your left hand. This will help prevent camera shake from a heavy lens, and it will keep your fingers out of the way of the lens and LCD screen.
Stand up straight! If you're taking shots standing upright, make sure you don't slouch. Keep your back straight ... unless you want to spend a fortune with the osteopath in later years! Try to keep your elbows as close to your body as possible to aid stability. Aim for a nice wide stance with your feet, and you'll end up with better stability and far better shots.
Use your knees. If you need a lower angle of view, crouching down on one knee is the way to go. Not only will you lower your perspective, but this position also aids stability. Make sure you rest one elbow on your knee, though, or you'll be flailing all over the place!
Use the viewfinder to frame your images. If you try to use the LCD screen to compose your photographs, then you'll have to hold the camera at arm's length. This immediately takes away stability and could cause camera shake. All pros use the viewfinder, so follow their lead!