Take down any canopies. Some queen-sized beds have canopies. A canopy is a covering that fits over the top of side posters placed on the headboard and footboard of the bed. Remove the fabric from the canopy and store it in case you want to use it again.
Remove the headboard and footboard. Many queen-sized beds come with sideboards in the front of the bed and at the foot of it. You should be able to remove them from the railings with a screwdriver. Store the boards and any screws where you can easily retrieve them. You should be left with standard railings that will hold up the bed from the floor. You may find that removing the boards causes the bed frame to fall apart. In that case, you can leave up the boards.
Place the queen-sized bed against a wall. Most daybeds are placed against a wall without a window and they are not left freestanding. Avoid placing the bed against a radiator or cooling system. You can leave any pictures on the wall if they don't touch the bed.
Cover the bed with bedding that resembles material used for a couch or chair slipcover. Many bedding stores stock items that are designed to be on a daybed. If you don't find a size that you like, then you can commission or make your own larger bedding materials.
Purchase bolsters. Bolsters are large pillows designed to be placed next to the wall so that you can relax when sitting on the bed. The bolsters should coordinate with the bedding used to cover the bed. Use enough pillows to cover the top of the bed on the side where it meets the wall. If you still have a headboard or footboard on the bed, then you should also place bolsters against both pieces.
Add details. Toss a few well-chosen throw pillows on the top of the bed to coordinate with the bolsters.