Tape off the edges of the trim with painter's tape and newspaper, covering the surrounding wall and floor. Put on rubber gloves.
Brush chemical stripper onto the surface of the wood, working in sections of 2 or 3 feet. For each section, let the stripper sit on the paint until it starts to wrinkle and soften, usually about ten minutes.
Scrape off the softened paint with a plastic putty knife, pushing the knife with the grain of the wood. If the paint doesn't come off easily, add a little more stripper and let it work for another few minutes.
Scrub the wood with nylon wool as you scrape off the paint, to pull the residual paint. Wipe down the wood with paper towels.
Let the surface dry completely after you've stripped all the paint. Go over the wood with a vibrating detail sander, to take off any residual dried paint and to get the surface clean and smooth. The trim is now ready for refinishing.