Decide whether to use a platform bedframe or place the mattresses directly on the floor. If your ceilings are standard height or higher, the platform can provide a more substantial foundation. However, many small apartments have low ceilings, and keeping furniture low can help make the room look taller.
Position the platform against one wall, and set the box spring on top. If you are not using a platform, push the twin box spring against this wall. Place the remaining mattress atop the box spring, and align all of the edges.
Fit the tailored rectangular slipcover over the mattresses together. Alternately, you can dress the mattresses with sheets, a bed skirt and a coverlet if you do not mind it looking more like a bed than a couch. Keep the look as uncluttered as possible.
Line the back of the convertible couch with pillows propped against the wall. You can use numerous smaller pillows or a large bolster pillow. When you have a guest, remove the pillows and the slipcover, if you use one, and use the mattresses as a bed.