Using a clarifying shampoo, wash your hair every couple days at least. You'll know your hair is clean when it "squeaks" and all traces of added residue are removed.
Only use a dime-sized amount of conditioner. Alternatively, don't use conditioner at all, or use it infrequently, say, once a week. If your hair is longer, just use the conditioner on the length (say, from the ears down) and keep it off your scalp.
Be choosy about the styling products you use. Don't use too much or you'll weigh your hair down and residue could accumulate. Stay away from gloppy gels, because they will make your hair look greasy when it's not!
Try a product like CitraShine or Garnier Fructis to add extra shine to your hair.
Brush your hair regularly since this helps distribute a glossy sheen throughout your tresses.
Rinse your hair with cold water. Warm or hot water starts to form oils immediately, and will make your hair frizzy.
Cut split ends of hair. It will help keep your hair from becoming more damaged. It will appear thicker and strong. Also, If you don't do it sooner you'll have to cut off more of it later. (split ends get worse!)
You can use baby powder or other types of powder to make your hair look less greasy by rubbing it in to your roots, but don't put too much in so that people can see whiteness on your hair.