Wipe up the remover as quickly as possible. Depending upon the makeup of your nail polish remover, it may not damage your wood if you remove it immediately. Using a soft cloth, wipe up the remover immediately after the spill, leaving the table to dry and the finish to re-harden if the polish has softened it.
Sand the impacted area. If the polish remover left your finish bubbled, you will have to sand away the marred finish and remove it to create a smooth look once again. Use a fine, 220-grit sandpaper to remove the finish from the impacted area.
Inspect the stain for damage. Unless your nail polish remover sat on the table top for an extended period of time, the stain that rests under the protective top coat is likely unmarred. If, upon inspection, you find that the table is discolored, your only option to ensure a perfect match is to sand and refinish the entire piece. If the coloration appears unaffected, you can simply replace the top coat.
Remove the dust that collected on the table from sanding, using a shop vacuum. Take care to remove all the dust as any remaining particles will mar your new finish.
Apply clear polyurethane to the sanded area. Using a paintbrush and working in the direction of the grain of the wood, apply this new top coat. Apply the coat more thickly in the areas in which you sanded directly and more lightly as you move to the edges of the impacted area, as you are trying to create a seamless line between your new and your old top coat.