Remove as much of the unwanted surface materials as you can manually, using scrapers or chisels. Thoroughly clean the floor surface with a broom and then vacuum it with a shop vacuum.
Install a tungsten-carbide insert in the grinder, following the grinder manufacturer's instructions. Tungsten-carbide inserts work best for removing materials thicker than 1/16 inch.
Turn the grinder on. Slowly lower it until the grinding surface is in contact with the floor.
Move the grinder from side to side to keep swirl marks from forming in the cement floor. Make a couple of passes over extra-high spots to remove them and make them flush with the rest of the floor.
Clean the grinder after finishing. First unplug it, then knock off the residue with a hammer. If the residue cannot be knocked off with a hammer, use a concrete dissolving product to thoroughly clean the grinder.