Fresh flat paint is easy to wipe off any surface with a soft, lint-free cloth. As you dirty one face of the cloth, switch to a clean one. When wiping paint off the wall, wrap the cloth around your finger to make sure you only wipe the drip and not the surrounding paint. Wipe gently. Paint over the wiped spot immediately to cover up any smudges.
Hard dried paint won't come off with a simple wipe. You'll have to physically remove these drips with the flat edge of a razor blade. Hold the razor blade at a narrow angle to the wall to avoid nicking the paint. Sand the spot in the direction of the drip with 220- to 400-grit sandpaper. Work carefully so that you sand as little of the paint outside of the drip mark as possible. Flat paint hides imperfections well, but if there is a noticeable mark, paint over the pot.
Windows near painted walls often fall prey to drips. The best way to remove dry paint drips is with a razor blade. Wet the window around the paint drip to lubricate the razor and avoid scratching the grass. If you have to scrape dried paint drips off near the edge of the pane, take care not to break the seal between the fresh paint job on the windowsill and the glass pane.
A metal putty knife wrapped in a rag -- one layer thick -- will get flat paint drips off most hard surfaces including wood and tile. Scrape with the putty knife at a narrow angle to the floor. Keep scraping until all of the paint is gone. Scrub up any flakes or residue with soap and warm water. On hardwood surfaces, use as little water as possible and wipe the surface dry with a towel.
Flat latex paint drips will come up with a little scrubbing with soap and warm water. Oil based flat paint requires turpentine or mineral spirits to get it off of surfaces. Use a soft, lint-free cloth to scrub. After all traces of the paint are gone, wipe the surface with fresh water to remove all traces of the cleaning solution.