If the veneer is in good shape and you don't want to remove, scuff with steel wool and clean with denatured alcohol for painting. Then prime & paint.
Do you want to paint it, or keep it it’s beautiful original finish?
General Finishes Gel stain is great if you're wanting to keep the original wood look (no sanding required). OR you can easily paint with chalk paint. (Also, no sanding required. :)
Here is a post on how to paint old furniture
You will need to strip off the old finish, and sand with the grain, after all the residue from the stripper has been thoroughly cleaned off.
Any veneer repairs need to be done then.
This is much easier to watch with YouTube videos, of which there are literally hundreds and hundreds of them. Look around for one that suits your particular level of furniture and your skill as well as you tools.