How do I strip a staircase handrail that has been painted & stained?

Try citristrip

You may have to sand it with a rough textured sandpaper and then a finer one to finish off the surface and make it smooth. You could use a paint stripper but that is toxic and messy.

Citristrip safe stripper. Scraping and sanding.

Saw this recently done on This Old House with a chemical stripper.

If you can remove it take it off do that and take it outside where you can be a little more messy, you just need to sand off any lumps or bumps and any glazy type surface. You should be able to paint right over what you sanded. I recommend sanding outside as it is horribly dusty.

I use citristrip also, combined with a little sanding for what doesn't scrape off.

Using a stripper is the way to go for this purpose. You may have to sand nonetheless, but the amount of work will be a lot less. Best of luck to you.

Thanks all soooo much!