Don protective clothing that covers as much skin as possible, for protection during the concrete grinding process. Include a respirator, safety goggles and work gloves.
Attach a 32-grit diamond pad to a concrete grinder, which can be rented from a home improvement store or equipment rental shop.
Move the grinder to the section of scratched concrete and, starting at the edge of the scratch, work the grinder in a small back and forth motion across the width of the scratch. Continue grinding down the surface along the length of the scratch until the sides of the scratch are level with the surface of the driveway. The scratch will still be visible.
Clear away any dust created by the first pass with the grinder.
Change the pad on the concrete grinder to a 60-grit diamond pad. Repeat the grinding passes on the scratched surface, this time removing the rough edges of the scratch.
Clear the dust left from the grinder, and then spray a coating of reactive concrete hardener onto the repaired area. As you grind the surface of the concrete you open small holes in the cement, aerating the concrete; the hardener reduces the effects of the aeration.
Change the grinder pad to a 120-grit diamond pad and make a final pass along the scratch. Grind away the last traces of the scratch, leveling the surface of the concrete.
Remove the grinder and apply a coating of slip-resistant concrete sealant to the entire surface of the driveway. Use a low-nap roller to apply the sealant. Allow the sealant to dry for the amount of time suggested by the sealant manufacturer, before using the driveway. The slip-resistant sealant has an additive that increases traction on the concrete.