Mix a mild soap (like dish soap) with warm water in a pan or bucket. Make sure you have several cleaning cloths (not paper towels or other products that could tear apart when they get wet).
Dampen the cleaning cloth in the soapy water and ring the cloth out, so it's not dripping wet. Gently wipe down the top and sides of the deep freezer. Be sure to not get water on the coils and don't directly wipe down the coils, as that could cause damage to the freezer.
Pull the freezer out from the wall so you can properly clean around the back of it. Using the vacuum, use an attachment nozzle to get the dust and dirt away from the vents of the freezer. These are usually located around the back or underneath the freezer. Be very careful when cleaning around the coils, so you don't knock them loose.
If there is a lot of dust and dirt around the coils that the vacuum can't pick up easily, use a static dust-attracting cloth to gently wipe the area around the coils and pick up the dust and clean some of the hard-to-reach parts.
Spray the top and side surfaces with an anti-bacterial kitchen cleaner spray. You may need a spray that cuts through oil if the freezer is greasy to the touch. Wipe the surfaces of the freezer down with a clean cloth. Push the freezer back into place against the wall.