How do I with common household chemicals?
Well that is a tough one because most paint removers/thinners will end up damaging the plastic. but one method you can try is to use Rubbing Alcohol. First- gently scrape as much of the paint off as you can with a blade. Next, pour rubbing alcohol over what ever paint was left over from the previous step. I would suggest letting it sit for 5-10 minutes (you will need to put more alcohol on it regularly because alcohol evaporates fast) Then you will want to rub the area with paper towels to clear off the remaining paint. Finally give it a good wash with warm water and dish soap and one more quick scrubbing with a sponge (or my personal favorite a - Mr. Clean Magic Eraser) and that should give you a good result. If that fails try to use a Goo Gone or Goof Off. These are both found at mostly any hardware store and are actually quite effective. Well I hope this helps and I wish you the best of luck. - Adam -
Usually, you can scratch it off. Try a butter knife.
what kind of paint and what kind of plastic
without the chance of damage to the plastic you can try apple cider vinegar and scrape with a popsicle stick with the end cut off on a slant like a sharp edge. There's no scratches with it. Hot full strength apple cider vinegar will take off paint and varnish.
some paints will chemically bond with the plastic, in which case you cannot remove it...try a scratch test to see if it chips off or not. If you could add some detail to your question, we might be able give you more help