Dust the wreath carefully with an electrostatic duster, which is designed to attract the dust. A feather duster also works well, provided you shake it outdoors often.
Lay out newspapers and place the wreath on top, and then spray compressed air on it. Start far out, about 18 inches, and work your way closer if necessary. You do not want to blow off any delicate parts, such as dried flower petals. You can also do this outdoors.
Blow the dust away from a wreath with a hair dryer set on low. Do this over top of the newspaper or outdoors.
Moisten a rag with water and wipe a plastic or vinyl wreath to remove caked on dust and debris.
Vacuum the dust off. If the wreath is not delicate and will not easily fall apart if you vacuum it, use the brush or wand attachment and vacuum.