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Rub the sandpaper in circles, pressing firmly. Sand a little beyond the original damage, even if it means peeling away a small amount of clear coat that is still in decent condition. If the pigmented paint below the clear coat is still in good shape, don't scrub so hard that you remove it as well. If the clear coat is already gone, skip this initial sanding and go straight to wet sanding and cleaning. Use 2000 grit sandpaper that's been soaking in water for an hour. Smooth out the transition lines between your repair area and the surrounding clear coat. Keep the sandpaper wet by dipping it in water as needed. Straighten out or square off the work area when you can, as this will make it easier to tape off the area later. Use an alcohol-based cleaner, like glass cleaner, to clean the area you just sanded. Follow this up with a solvent-based paint prep cleaner, which will either come with your chosen clear coat repair kit or be found alongside the clear coat sprays. These pads are similar to the ones you might use on your dirty pots and pans in the kitchen, and are available at automotive supply retailers. Don't use steel wool or sandpaper. You just want to give the pigmented paint a slightly rough texture. Clean the area afterward with the solvent-based cleaner. Skip this step if the paint is already scuffed up from your earlier sanding. Stick the tape to your pants and peel it away once or twice to make it less sticky. Create a taped-off area around the removed clear coat that's slightly larger than the actual damaged area. Use plastic sheeting and more tape to expand the outside of the protective zone, so that your clear coat spray only lands on the car where intended. Shake the can as instructed on its label. Also refer to the label for the optimal spraying distance and motion. Keep moving as you spray so that you create an even layer. Let this first coat dry for at least 5 minutes, or for the time recommended on the can. You may be instructed to go over each dried coat with very fine sandpaper (e.g., 1500 or 2000 grit, possibly soaked with water). Follow the instructions on the spray can, and wipe away dust and debris with a tack cloth. Two coats is usually sufficient, but follow the instructions on the can. Let each coat dry for at least 5 minutes before applying the next one. Remove the tape and plastic sheeting after the last coat dries. Wait several hours, or overnight, before finishing off the repair. Lightly go over the repaired area with 2000 grit sandpaper. Then, use a polishing compound and a motorized buffer to blend the transitions and make your repair work vanish as much as possible. Buff the area by hand if you need or want to, but expect to have a sore arm the next day!

Summary:
Scrub the damaged area with 1000 grit sandpaper. Wet sand the transition between your work area and the remaining clear coat. Clean the clear coat-free area with alcohol and solvent-based cleaners. Scuff the cleaned area with a fine grit, woven scuffing pad. Tape off the work area with easy-to-remove masking tape. Spray the aerosol can of clear coat onto the surface. Apply a second layer of clear coat in the same manner. Blend in the repaired area with the surrounding car finish.