Spilling fingernail polish on anything makes a hard-to-remove mess. House paint usually washes off, but nail polish is tougher. With most stains, the best results are achieved if the spill is treated right away. The few cleaners that work on nail polish are polish remover, Spic n Span and rubbing alcohol.
If possible, can get to the stain right away. Wipe up as much of the polish you can without rubbing it into the fabric. Then use nail polish remover on the remaining polish. Dark polishes will come out but leave a color residue that may come out in the washer. When the remover has loosened all the polish, wash the comforter in the washing machine.
Sometimes you might find dry fingernail polish on comforters, perhaps from when a little girl decided to paint her own nails. When this happens, it probably will take a stronger remover to get it out. First try any polish remover. If that doesn't work, look for a remover with a high concentration of acetone. Salons use full strength acetone to remove acrylic nails, so inquire at a local salon.
Use cotton balls and gently rub the polish to loosen and remove it. Then wash the comforter to wash out the polish remover. You can also try Spic N Span with a sponge or rubbing alcohol on cotton balls. Hydrogen Peroxide can also lift some stains out.