Furniture, Wood and Cabinetry Finishing - Refinishing vintage coffee and end table set

I recently received a coffee and end table set from a relative which I believe is from the 1970s. Each piece has aged differently, and I would like to refinish them. They are finished with a wood veneer, and I'm not sure how to go about removing the sealant and how to prepare the surface for re-staining.
The pieces are in excellent condition with the exception of one small dent in the surface of the coffee table, but I don't believe this would bother any sort of restoration process.
Originally I was going to use a fine grit sandpaper to remove the topcoat, but upon researching, I discovered sandpaper is probably not the best option.
These tables are great, and I'd really like to go the proper way in refinishing them.

Thanks for any advice.

Any good 'stripper' i.e. paint and varnish remover will get the surface ready to restain. Just follow the directions on the can.

You might want to search this forum for more detailed instruictions on stripping/refinishing