Should be fairly straightforward, you'll need to strip the finish, ideally with a Chemical stripper, gentle sand and wipe down with alcohol to make sure theres no contaminents left, oil liberally and wipe off with something like Danish or Linseed oil and then use an appropiate varnish or wax sealer.

I do reccomend searching those tutorials out so you can see visually how it's done, I wouldn't use a stain in this case if you're certain its Walnut as you'll not want to darken it (some like my 25 use Beech and then darken to mimic walnut).