Removing old paint from a wood stair railing isn't a difficult job, but it will require patience and preparation. Since chemical strippers require ventilation, it's not always an option for indoor stairs. Here is what you can do.
Step 1 - Prepare the Area
You want to protect the floors around the railing by placing drop cloths. It's best to pick a day where your home will have little traffic interfering. Clean and dust the railing.
Step 2 - Sanding
Use an orbital sander to remove as much of the paint as you can. This will prevent you from needing to use harsh chemicals, or at least as much.
Step 3 - Scraping
You can scrape away paint that the sander didn't get. If there is anything remaining, you will need to use a stripper.
Step 4 - Stripping
You want to use paint stripper as a last resort. If it becomes necessary, find a stripper that has low odor or is environmentally friendly. If this isn't possible, you will want to use a good quality respirator, and open all the windows in the house. Apply the stripper according to the directions on the packaging. It should only take about 15 minutes to work, then you can remove the excess with a clean cloth.