How can I refinish antique wooden tables?

If there are deep scratches , you'd probably be better off sanding it anyway . Start with a 180 grit and work up to 220. Lots of elbow grease , but it'll be worth it in the end .

i agree sanding is the best and if you have access to it an electric sander works great and saves on sore hands.

Citristrip is a very effective stripper. You will still need to sand before restaining or painting.

I use R.A.P. stripper. It's made in Bay City, MI and contains NO water unlike Citristrip and other Big Box products. No water means it is safe for antiques. There are 2 versions - thick and thin. The thick is like a loose jelly and the thin is a thin liquid. This product will remove everything down to bare wood in a VERY short time. I refinished all kinds of wood furniture with it and loved the results. In fact, I stripped bookcases that had 6 coats of paint, including two coats of Kilz. RAP is so fast that by the time I finished applying the product to a shelf, the first part was already mostly ready to scrape off. It's also water cleanup and won't eat your flesh. I would wash down the project after stripping and allow it to dry for a day or two before sanding and any other refinishing. Hope this helps

Sand it, prime it, then paint using the color of your choice.

P.S. make sure to use a clear coat to protect your paint.