Choose a location that is low in humidity to store couch pillows. A closet or under a bed, for example, may be ideal locations for pillow storage, but the basement may not.
Air dry pillows if necessary. Do not store pillows that are even slightly damp.
Store couch pillows---in a bug-free environment---in extra pillow cases or other breathable sacks. In areas where bugs are a concern, especially bed bugs, store pillows in sealed plastic bags, but only if they are completely dry.
Put pillows in a chest or a coffee table with storage if you plan on using the pillows frequently and want to be able to pull them out to use on occasion.