Set as many floor fans as you can get your hands on in the room. Aim each fan at a different wall in the the room. Turn the fans on the highest setting to get the air flowing.
Turn the home's furnace up to above 70 degrees F. This heat helps dry out the humidity in the air. If the temperature outside is below 70 degrees F, keep the windows and doors in the house closed. If the temperature is above 70 degrees F, and the humidity in the air is below 30 percent, open the doors and windows. This will help speed up the drying process.
Check the drywall compound after 24 hours. If you still see grey coloration along the seams, it's not ready to sand. Wait until the compound has turned completely white before sanding.