Hand-wash removable shelves, wire racks, and drawers in hot water and mild dish soap. (Let glass components warm up to room temperature before letting them contact hot water; otherwise they might crack.) Cover stubborn food spills with a warm, wet cloth for a few minutes to soften them for removal with a nonabrasive scrubber. Pay special attention to the bottom of wire racks, which is a spot that attracts debris.
Cleaning the Interior
Wash inside your fridge with a mixture of 1 part baking soda and 7 parts water. (Beware commercial cleaners -- their scent might transfer to food.) Work from top to bottom to prevent drips from landing on already-clean surfaces. Use an old toothbrush or toothpicks to reach cracks and crevices you can't get to with a cloth, such as hinges and other hardware. Wipe everything dry with a clean towel.
Cleaning the Gasket
Pay special attention to the rubber gasket around the door. It needs to be kept clean and supple to maintain a tight seal. Use warm water and liquid dish soap for normal grime and a bleach-base cleaner if you find mold. Rinse thoroughly and wipe dry. Then coat the seal with a thin layer of petroleum jelly to keep it from drying out.
Don't give sticky spills a jump start by reloading the fridge with sloppy food containers and spoiled fruits and vegetables. Toss anything that's questionable. Use baking soda and water to wipe off any jars, bottles, or cans with drips or crusty lids. Make sure you use clean cloths and dry everything thoroughly before putting it back. Make this task easier by doing it as you go.