This is the most important step to preserving your decorative concrete floor. Dust mopping regularly will prevent sand and dirt from building up on the surface of the floor, abrading the floor finish, and wearing through the concrete sealer, and concrete stain, below. Dust mopping also removes an estimated 80-90% of indoor dust that serves as air pollutants, health hazards, and sources of allergies. Any light duty sweeping or vacuuming tool is fine, but we find an 18” to 36” microfiber dust mop works best. The static electricity created by this flat, broad-surfaced material picks up small debris and contaminants like a magnet. But make sure that your dust mop has not been treated with any oils, silicones, or cleaners by the manufacturer, and shake it out periodically so as not to scratch the floor.
Wooster Brush Company has a nice dust mop called the Dust Eater that is perfect for stained concrete floor maintenance. It is available online for about $20 here:
Wooster Dust Eater. You can also get the Norton BlueMagnet online for $20 at Integrity Supply, or from the Merle B Smith Company in Burr Ridge, Illinois, for about the same price. If you prefer a vacuum, Euro-Pro has a great new lightweight, vacuum called the Shark Vac-Then-Steam for hard surfaces, including concrete. It is slightly more expensive, at $120 from Overstock.com, but lets you avoid having to shake out a dust mop from time to time, and then allows you to "steam mop" and sanitize your floor, after vacuuming.
Note: When using a vacuum only, be more thorough, since dust pickup is generally somewhat less effective and complete than with a dust mop or broom.