Second to cleaning up drywall dust, cleaning up "dried up" drywall mud is tough.
After all, drywall mud is intended for the long haul. It is intended to help cover and keep seams secure for many years. If it was easy to clean up, it wouldn't really be doing its job, would it?
1. Avoid Mess in the First Place
Learn to not over-apply drywall mud. Anyway, the more mud you apply, the mud you will need to sand down later on. It doesn't take very much mud to do the trick.
2. Cover Surfaces
It's possible to drip small amounts of latex paint on some hard, smooth surfaces and later peel it off with your fingernail. But this technique doesn't work with drywall compound. Scraping will only take off your surface. Cover floors and furniture.
3. Clean Up with Seconds
Have a paper towel or rag with you at all times to clean up the mess. Don't let it sit more than a few seconds before wiping up.
4. Hot Water
For goopy, semi-set drywall mud, you can soak tools in hot water.
5. Scrape Dried Mud
Drywall compound that has dried will not soak off. You can soak your tools for days and still not soak it off. Scraping with another drywall tool is about the only way to go.
6. Last - Toss Tools
Tools can be scraped and soaked, but sometimes it's just too much. In some cases, you may need to accept the fact that a tool is no longer worth keeping.