What is the best way to clean antique wooden (pine) furniture?

Sometimes, the least done the better, so be careful. There are many fine products out there, but I use basic mild soap to begin with…then, beeswax.

Good old soap and water will be fine. You may have to sand with light sandpaper to flatten the grain back down. Once you’ve got it clean, paint or varnish to protect the surface.

Murphy’s Oil Soap works well, and gently.

My SO’s uncle is a French polisher, and he recommends water with a dash of soap, if need be. Like @augustlan , I’m a fan of Murphy’s Oil Soap.

What about applying some linseed oil after you’ve given it a wash down?

I’ve done that. It was on an 1800s mahogany (I think) dressing table. Worked like a charm.