To clean a griddle, pour a little room temperature water on the warm surface and scrub with a spatula or sponge to remove cooked-on food. Once the surface is clean, use a mild detergent and rinse well before re-seasoning the surface with a small amount of oil.
Never pour cold water directly on to a hot griddle surface. The temperature difference between the liquid and metal can cause the griddle to warp and bend, and may even cause cracks in the surface. The griddle should be allowed to cool down after cooking before any water is added, and the water should be at room temperature or warmer in order to prevent thermal shock.
If the griddle has a non-stick surface, seasoning is an important part of maintaining that quality. After cleaning, add a small amount of oil to the surface and rub it in using a paper towel. The oil bonds with the surface of the metal, improving its non-stick quality and preventing rust. This is especially important for cast-iron griddles, which should build up a distinctive black non-stick coating over a lifetime of use. Detergents can degrade this coating, so care should be taken to re-season the pan every time it is washed.