I found this for you. You're question sparked interest bc we are currently building and doing stained concrete. Although at times I'm sure you'll need to wet parts to get 'stuff' up, the directions do makes sense if you are just trying to get dirt and small debris off of the floor. Sounds easy enough to me :)
InstructionsThings You'll Need:
O'Cedar Floor Dust Mop
a couple of extra O'Cedar microfiber mop heads
Step 1 Purchase an O'Cedar Microfiber Dust Mop from any major store such as Wal-mart, Target etc... Be sure to buy a couple of extra microfiber mop heads.
Step 2You clean acid stained floors just as you would dusting a piece of furniture. The floor surface has been sealed, so it's just like dry dusting. I do not recommend wetting the mop head first. It's just unnecessary.
Step 3Slip the microfiber mop head onto the mop and begin dusting. You won't believe the stuff this will pick up. I dust my floors once a week. Extremely quick and easy. No pushing a heavy vacuum for me.
Step 4 Take the mop head off, throw it in the washer and it's ready to go again.
Step 5 I recommend resealing a stained floor every five years or so, especially in high traffic areas such as hallways.