Cover over small scratches with a scratch remover, a special felt-tip marker used to restore furniture. You can find these markers at furniture repair stores or craft stores. This works best with very thin scratches.
Rub a quarter-sized amount of automotive wax over the lacquer furniture to camouflage minor scratches if you cannot find a scratch remover. Apply the wax with a tack cloth. Re-apply a new coat of wax every couple months to keep the furniture looking blemish-free.
Dip a piece of 1200-grit wet sandpaper in a bucket of water if you need to remove a large scratch, or multiple scratches. Drag the wet sandpaper back and forth over the scratched area to sand down a layer of lacquer paint. Sanding through a layer of lacquer will make the scratches blend in, since the paint will be uniform again. Dip the sandpaper in the bucket of water to remove grit from your wet sandpaper and to re-wet the sandpaper any time it dries out. When you've sanded through the paint surrounding the scratches, stop wet sanding.
Dry the panel with a clean tack cloth. Squirt a dime-sized amount of polishing compound onto the wood panel. Rub the polishing compound over the wood with an old sponge to remove a fine layer of lacquer.
Wipe the polishing compound off with a clean tack cloth to remove the polishing compound. Wipe away all traces of polishing compound since it will continue to eat through the paint if left on.
Apply a coat of automotive wax to the furniture to restore the shine to your lacquer wooden furniture, working in the same manner as in Step 2.