Whether you have a dusty basement, garage or workshop floor, you want to use cleaning elements that are equipped to handle the amount of dust on the floor. Avoid cleaning routines that simply brush the dust around, as this will typically push the dust into the air-- and it will settle right back onto the flooring.
Sweep light dust build-up with a broom. Sweep in short, controlled motions to sweep the dirt into a pile without brushing the dirt up into the air. Wild sweeping motions will often just spread the dirt around. Collect and discard the dirt.
Vacuum the floors to collect thicker dust. If heavier chunks of debris are mixed in with the dust, use a wet-dry vacuum, which is equipped to handle heavier build-up in workshop areas.
Fill a bucket with warm water. Add in about 1 cup white vinegar per gallon of water if you want to clean the floors as you remove the dust.
Dip a cleaning mop into the solution and wring the mop out.
Wipe the mop across the dusty floor, dipping back into the solution as needed to rinse the mop and collect new solution. The damp mop quickly collects the dust without spreading it into the air.