You could try using a scraper to remove the veneer and a sander to finish the job. Sometimes the veneer comes off easily, sometimes the glue is tough and needs to be softened. A hot iron over a moist rag can be used to steam off old veneer if the glue is an old-fashioned kind of animal product. It is a trial and error kind of process, with a serious potential for damaging the surface underneath. You might have good enough wood beneath the veneer to stain, but you might need to settle for painting it. You might even need to reapply veneer.