How to remove old lacquer, shellac and stains from wood furniture?

Citristrip stripper.

Any commercial paint stripper

I agree with William - I only use Citristrip. Less fumes, safer.. I would recommend you scrub it before stripping, since an instructor I once had taught me "don't waste stripper, cleaning off dirt". She was right, and every piece I've done since then, I've scrubbed down before stripping it. No matter how clean it looks before you start, you will be scrubbing off years of use.

The best way is wth a metal scraper they they come in difference shapes and it doesn't affect the wood as you are not using any chemical. You do have to sharpen them regularly.

removing old crud I prefer denatured Alcohol/water; will not leave residue as does detergents ( not just 'Dawn' ) and/or Baking Soda ....