The easiest way to do that is to use Mineral Spirits and elbow grease.
The cause of this was that we used some old varnish on the picture frame from last month and it never quite dried. It always had a tacky look to it and seemed like it was never going to look good. Sandpaper made scratch marks and stronger chemicals would have stripped the paint off entirely.
Using some old rags and some mineral spirits I was able to remove little bits at a time and get a really good "antique" look. The mineral spirits aren't strong enough to make a huge mess but rather make things look weathered.
You can see the work progress in the photos.