Electric griddles are convenient for many reasons. They provide an extra cooking surface in your kitchen, for example, and are portable. Cleaning an electric griddle is not typically difficult, even if you burned some food onto the surface. Some brands of electric griddles are even dishwasher safe, although you should always check to make sure yours is first before attempting this--if the cooking surface can be lifted out of the housing (leaving behind the electrical components) then it likely is.
Unplug the griddle from the outlet and let the griddle cool down before touching it. Carefully remove the drip pan, if applicable (some models have a tray or pan and others simply have grooves where the grease collects). Place this in your sink to clean separately.
Wipe the surface of the griddle with paper towels to absorb extra oils. Keep doing this with fresh paper towels as long as you are still retrieving oil.
Wet a non-abrasive sponge in warm water. Wring out excess water and pour a few drops of dish detergent on the sponge. Scrub the surfaces of the griddle with this sponge. If there are areas of burnt on food, add extra dish detergent to these areas and let it sit for a while (up to half an hour).
Rinse out the sponge and dampen it again with warm water. Rub this over the griddle to remove some of the detergent. Repeat this until no more suds appear on the griddle.
Dampen a cloth and wipe this over the griddle to remove any leftover traces of detergent. Allow the griddle to air dry until the next use.