Fold up the feather bed into a big square. Start at the bottom of the bed and fold the first third up. Kneel on the folded part to help the compression process. Place a small sachet or a few dryer sheets on the top of this fold. This will help reduce the "gamey" smell that can accompany feather beds when they are stored. Go to the top of the bed and fold the second third down. You should now have a big rectangle. Kneel on the bed again. Fold this rectangle in half. You now have a big square.
Place the bed in a breathable storage bag. Do not use a plastic bag. This will encourage moisture, and odor will be a problem as well. Stuff the feather bed into the storage bag and then seal it as per manufacturer instructions.
Attach a vacuum hose to the storage bag. You will need a vacuum that has a reverse switch in order to suck the air out. Most canister vacs have this feature. In a pinch, you can also use a shop vac set to reverse. Turn the vacuum on and suck out the excess air from the bag. You should now have a much more manageable square.
Store the bag properly. Do not place the storage bag where it will be near any moisture. A cool and dry closet is ideal for storing a feather bed.
Decompress the feather bed. When it is time to use the feather bed again, take it out of the storage bag and unfold it. Fluff it up in the air and then give the feathers time to air out and fluff back up. Typically, a few hours is more than enough to decompress the bed.