Lightly spray the dust to make it damp (not wet), use a soft broom to sweep up as much as possible, and then vacuum. Drywall dust can easily clog household vacuums, so it’s best to use a wet/dry ...

Use a vacuum, not a brush ... and they have higher filtration to keep out drywall dust particles. You can get them with a pair of goggles to keep the dust out of your eyes for about $20.