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Place a box fan in the window. Remove and cover the furniture. Sweep the dust to the center of the room. Suck up the dust with a Shop Vac.
Point a box fan so that it pushes air out of your apartment. This will remove the dust from inside of your house. Turn the fan to high and let the dust in the air escape the room. As you continue to clean the dust, keep the fan on so that the drywall dust that you sweep up can be blown out of your house. Before you start disrupting the dust in the room, it's important that you empty the space of furniture. If you don't, the abrasive dust can settle on your furniture and hurt the finish on your belongings. Remove what you can out of the room and put it in another, dust-free room. Lay dropcloths or plastic tarps over furniture that's too large to move in order to protect them. Gently walk a push broom around the perimeter of the room and work your way into the middle. Make sure to be gentle and avoid pushing the dust up into the air. Use long stroking motions when pushing the dust around and try to create one pile in the center of your room. A Shop Vac or wet and dry vacuum cleaner has a larger carrying capacity and can pick up more dust than a traditional household vacuum cleaner. Start by vacuuming up all the dust that you managed to gather in the center of the room. After the initial dust is cleaned, continue to go over the entirety of the floor to suck up the remainder of the drywall dust.  Go over the floor again if you notice that your Shop Vac didn't get all the dust on the first vacuuming. If you don't have a Shop Vac than you can rent one from a department store. Make sure to use a HEPA filter to trap all of the drywall dust when using the Shop Vac.