Wipe wet paint splatters off the wood with a moist rag as soon as you make them. Wet paint splattered on wood requires little effort to clean; a moist rag will wipe it away with ease.
Scrape hardened paint splatters off the wood with your fingernail or a razor blade. The fingernail method works well because you can scrape as hard as is required without causing damage to the wood. If you use the razor blade, be careful and meticulous to avoid gouging the wood.
Sand the paint splatters off lightly with 180-grit sandpaper. Too much vigorous sanding could ruin the finish of the wood and require you to apply more paint or varnish, which is time-consuming. Careful, light sanding will remove the paint marks but leave the wood's finish intact.
Dab a cotton swab into a jar of paint thinner, and lightly rub the swab on the paint splatter. The paint thinner will help loosen and lift the paint's hold on the wood, enabling you to wipe it with a rag.