How do you get paint off a wooden table without damaging the wood?
It depends on how much paint you're talking about. If it's just a little, you can try gently scraping it, but it still could leave scratches. If it's a lot, you may have to use paint thinner or stripper and then you're refinishing the wood.
Try a product called Circa 1850.
It's a gel like stripper, works great on one layer of paint or many layers. Just brush it on, let sit @2minutes and use a scraper to remove the paint. The paint will come off with ease. Then wash the wood with a little soapy water. This stuff works awesome, but put in a metal tray and if possible do it outdoors. It will not harm the wood.