Whether you have a vinyl or linoleum floor -- and the two can be difficult to differentiate -- a wet paint spill usually isn't anything to worry about. Linoleum has a hardened linseed oil finish similar to a wood finish, though, and removing a hardened paint spill can be problematic. You can use steam, but only if the linoleum is relatively new and thick. Before doing this, try chipping the paint with a plastic implement.
Wipe the Spill Quickly
Whether you spill latex or oil-based paint on your linoleum, you should wipe it up as soon as you can. If you can get to it while it's wet, you'll be able to dab most of it with an absorbent cloth or paper towels. If the spill is latex paint, wipe off the residue with soapy water, and use alcohol if the paint is oil-based. Nail polish is a lacquer-based coating that you can remove with nonacetone-based nail polish remover or with acetone; test the acetone first if your floor is vinyl -- it may dull the finish. If so, use alcohol. Remember to keep your room well-ventilated when using solvents or isopropyl alcohol.
Chip and Scrape
If you don't get to a paint spill before it begins to harden, you can make the situation worse by trying to wipe it off. It's better to let the spill harden for a day or two so you can chip it off. Use a plastic paint scraper or putty knife for this -- a credit card is also effective. Tap the implement gently with a hammer to loosen hardened paint. Once the bulk of the paint is gone, clean the residue with soap and water or mineral spirits.
Softening Paint Splotches
Dried paint that isn't thick enough to break needs to be softened with steam or a solvent that's safe for the linoleum finish. To steam the paint off, set a clothes iron to a full-steam setting, place a damp towel over the spot and heat the towel with the iron. As a safer alternative for old or fragile linoleum, use isopropyl or denatured alcohol to soften dried latex and oil-based paint. Alcohol shouldn't harm the surface of linoleum, but you should test it first, and if it's safe, use it liberally, soaking a cloth or cotton swab and rubbing vigorously. If neither steam nor alcohol work, try nonacetone-based nail polish remover or -- as a last resort -- acetone, after testing it first.
Scrape With a Razor Blade
Some paint splotches may not soften with any solvent -- this is especially true for old ones -- and you may have no alternative but to scrape them with a razor blade. To avoid taking off part of the linoleum finish with the paint, it's better to scrape over the surface of the paint rather than trying to work the blade underneath it. Put a sharp blade into a razor knife and run the blade lightly over the surface of the paint until most of it is gone, then clean the residue with alcohol or soap and water.