Wipe down the scratched area with a soft rag dampened in warm, soapy water to remove surface dirt and dust. The area must be completely clean, or your repair work can create more small scratches by rubbing microscopic grit into the clear coat.
Dry the surface with a lint-free towel and inspect it to ensure that you have removed all dirt and dust. Wash the area again if necessary, and let it dry completely before continuing.
Rub a contrasting color of shoe polish or similar material into the coat. For example, on a white car, coat the scratch with black shoe polish. Fill in the scratch completely to help the damage stand out and create a guide to ensure you do not do further damage to the surrounding clear coat while you work.
Wipe excess shoe polish from the surface with a damp cloth. Wrap a piece of ultrafine (2000- or 3000-grit) wet/dry sandpaper around a sanding block. Fill a bowl with cold water and add two to three drops of liquid dish soap. Soak the sandpaper in the cold water for 10 minutes to lubricate the surface of the sandpaper, creating a more accurate and careful sanding tool.
Lightly sand the scratched area, working in back-and-forth and up-and-down strokes from all directions across the entire area to avoid sanding one area too low. Rinse the paper in the cold water any time it feels like the sandpaper is beginning to stick to the surface.
Work slowly, stopping every minute or so to inspect the scratch. Sand only until the shoe polish has disappeared. Sanding brings the surrounding paint even with the scratch in the clear coat, creating the look of a completely flat and undamaged surface.
Dry the area with a lint-free cloth and inspect the surface. You should be unable to see the shoe polish or the scratch. Sand some more if necessary.
Spread a thin layer of rubbing compound onto a terry cloth. Polish the area you sanded with the cloth, working in a circular motion to remove the tiny scratches left on the surface by the sandpaper.
Buff away haze left by the rubbing compound with a clean terrycloth. Wipe away any residual compound with a clean rag and rinse the area with clean water. Inspect the surface. There should be no more haze or scratches.
Polish the area once more with extra-fine polishing compound or swirl mark eliminator, which will prevent rag marks on the surface.
Seal the repaired area with car wax, applied with a soft applicator or cloth, to protect against further damage.