How to Paint Strip Stair Spindles

This process will vary depending on finish and material you are stripping.
I will concentrate on paint over wood.

Begin by choosing your method of finish removal. Sanding is effective, but can remove detail and leave an uneven surface.
Chemicals are effective and will strip to bare wood, but can be messy. Heat guns also work well, but can create fumes.

I have employed all three techniques with success.
Begin by heating the finish with the heat gun. Once the paint or Varnish begins to bubble, carefully scrape it with a DULL flat scraper. The finish should come off in large ribbons. A drop cloth will protect the floor.
Be aware of flammables in the area, including clothing. The heat gun is not an open flame, but the temperature is high enough to severely burn or start a fire.
Work slowly and with good ventilation. Don't worry about getting every bit off. Get the big chunks and clean your scraper often.

Once you have stripped as much of the finish as possible, clean up the area and let the woodwork cool off.

The next step involves a gel chemical paint stripper, brass soft bristle brush and some medium or fine sandpaper.
Intricate detail and tight areas can be cleaned up with the chemical stripper. Again, gloves, a mask and drop cloth are important. Don't forget ventilation.
If the heat gun did it's job, the soft bristle brush and sandpaper should finish the surface for a new coat of varnish or paint.
A Scotch-Brite pad and solvent will help remove residue.

With any finish removal, be aware of safety and health concerns.

Old paint can have lead and other chemicals. Lead test kits are available at most home improvement and hardware stores. Lead paint should not be disturbed especially if children are present!
Watch out for burns, skin irritation and toxic fumes. And be mindful of what you are doing! Eye protection, gloves, respirators or at least a dust mask and a shop vacuum with a good filter should be considered necessary.