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Rent a concrete grinder from your local home improvement center. Clear off your basement floor. Put on safety goggles and a respirator before you start. Spray your basement floor with a hose if you want to wet grind the concrete. Plug in your concrete grinder and turn it on. Push the grinder back and forth from one side of the floor to the other. Repeat going in the opposite direction to create a crosshatch pattern. Let your basement floor dry if necessary and then vacuum up any dust.
Most home improvement centers have concrete grinders you can rent out for a project so you don’t have to buy one outright. If you’re not sure whether a store near you rents them, call ahead and ask before you go in. When using a concrete grinder, it's important that the floor is completely free of any obstacles or debris. Remove all of the appliances and furniture in your basement. Then, go over the floor with a vacuum to pick up any dirt or dust. When you’re grinding concrete, small particles of concrete can be thrown into the air. These particles can be dangerous if they get in your eyes or lungs. It’s important that you wear safety goggles and a respirator at all times when you’re using a concrete grinder. You can find safety goggles and a respirator online or at your local home improvement center. You can either dry grind or wet grind your floor. Wet grinding is preferable because the water on the floor soaks up the concrete dust and leaves less of a mess to clean up later on. You don’t have to wet grind your basement floor, just keep in mind that you’ll have a bigger mess to clean up if you don’t.  Read the manual that came with your concrete grinder to make sure it’s compatible with wet grinding. If you decide to wet grind, spray your basement floor with enough water that there's a visible puddle across the entire floor. Make sure all of the proper attachments are in place so it works effectively. You should also read through the user’s manual that came with the grinder before you turn it on. When you reach one side of the floor, move the grinder over next to the row you just made and then slowly push it back to the other side to make a new row. Continue doing this until you’ve gone over the entire surface of the floor.  When you encounter a raised spot on the floor, hold the grinder over it for a few seconds so it grinds it down. Make sure you’re pushing the grinder in a straight line. Once you’ve gone over the floor once with the concrete grinder, it’s important that you go over it a second time in the opposite direction so that the floor is even. Do the same thing you did the first time you went over the floor, only this time push the grinder perpendicular to the rows you just made. If you wet ground the floor, you’ll need to let it completely dry before you clean it. Otherwise, you can start vacuuming up the dust right away. Once your floor is clean, you can move any furniture and appliances you took out back into the room.