Are there any tips to prevent or reduce dust when working with drywall?
Here's one small tip: use a sticky note to catch dust from drilling- (courtesy of: http://rebrn.com/re/lpt-use-a-post-it-note-to-catch-dust-when-drilling-2615252/)





Another tip (for cutting into the ceiling) might be to use a piece of paper or a styrofoam cup to create a cone- taped around a drill or sawzall- (How to avoid dust when drilling in the ceiling)
Of course attaching a vacuum hose to the tool might work, or it might be so cumbersome that it's not really worth the struggle. Many sanders have a vacuum attachment built in.
It has been suggested in a few places that a bit of shaving cream or toothpaste can be applied at or near the area to collect dust.
Making cuts with a razor or box cutter is less dusty than a key-hole saw or a sawzall.
Obviously, a drop cloth will be necessary, especially for sanding.
Open two or more windows (so that air can flow through the house) and set a box fan in the window closest to the area where dust will be generated, blowing outward.
Many vacuums will not have fine enough filters to capture all of the dust. So a dust collector might be handy to use in conjunction with a vacuum.





Wetsanding is a technique where you use a damp sponge or damp towel to sand patches.
And there are low dust drywall compounds (muds).