1) Turn off your refrigerator. This can keep you from getting electrocuted while cleaning the fridge by any chance. Try turning it off 20 to 30 minutes before cleaning it. This will allow the freezer to defrost which makes cleaning much easier.
2) Clear everything out. - Remove all the food items inside. Put the highly-perishable ones in a cool bag immediately.
3) Wash its door and insides with warm soapy water. Dissolve ample amount of dishwashing liquid in a basin of lukewarm water. Use a sponge or a soft cloth rag for washing your fridge up.
4) Don't forget to pay special attention to the bottom and top parts inside. Hard stains could be hiding in them. Check the door seal too. Gently clean the door seal with a toothbrush or a damp cloth. Be careful not to damage it.
5) Rinse it well and let it dry afterwards. You can use a soft cloth or paper towel to dry your fridge. Don't put your food stock back in the fridge unless it is totally dry.
6) Clean its exterior once in a while. If your fridge is enclosed in a cabinet, pull it out every now and then. Wipe its top and sides. Sweep or vacuum the floor underneath your fridge. If stains and stench have accumulated underneath, clean the floor with bleach and water solution. Bleach will help remove the stain and the stinky smell.
If you want to take your fridge cleaning a step further, watch this instructional video I stumbled upon online. All credits to the owner.