The old standby method for cleaning a cookie sheet, and the method that most often works, is to soak the pan in warm soapy water for a least 30 minutes. Use a bench knife or a rubber scraper to carefully scrape off the food. Remember not to use a bench knife on a nonstick surface.
Another great trick is to use oven cleaner on cookie sheets. Spray sheet with cleaner and let it sit for about 15 minutes, then wipe down and rinse clean. Make sure to use the oven cleaner in a well ventilated area. Check the cleaner's label to ensure it will not damage the surface of your cookware.
It may sound odd, but you can clean cookie sheets and other pans using dryer sheets. Cover the bottom of the pan with warm soapy water, and then add a dryer sheet or two to the water. Wait for 15 minutes or so and the pan should clean up easily. It will also be static cling free.
For a serious grease problem, some people have had good luck using a grease remover made for automotive purposes. These products are heavy duty solvents and should be used with extreme care. Always check the label for any warnings.
A lot of people swear by the use of shampoo when it comes to getting grease and oil off cookie sheets. Most shampoos are mild (they are made to go on your head, after all) and will not damage metal.
To get stubborn stuck-on foods off your cookie sheet, you may want to try using another food product. Try soaking your pan in a high-acid cola drink. The acid and carbonation work together and can take care of quite a few tough clean up jobs.
To take care of grease, sprinkle the pan with some baking powder. This little wonder powder is fantastic at absorbing everything from grease and oil to problem odors.
No matter what you are trying to remove from your cookie sheet, remember to use a non-abrasive cleanser. Also remember to use great care when trying to get stuck-on foods off non-stick surface (despite the name, it does happen from time to time); never use a metal instrument to scrape a non-stick surface.
More information on cookie sheets