Oh its not that big of a deal really.
You are going to need a garage or an outside... because if you try this in the kitchen if you have a wife... you won't for long. At best you'll get the couch.
Rubber gloves are a must, you are going to need some varnish/paint STRIPPER (not thinner) which is availble at HD or Lowes for about $10 a quart. You'll also need a stripper pad and or some course steel wool. You can use fine sand paper, but be careful around your edges and checkering! There is really nothing you can do to tighten up your checkering.. assuming you are the average joe that is. I'd imagine if you knew how to checker, you wouldn't be asking about stripping varnish.
Directions on the back of the stripper container tell the whole tale. You can select your own finish... dark or light... up to you. I've used everything from birchwood casey stuff to regular old miniwax. Both look great. If you want some extra protection from the elements, use some type of polyuethane (they come in everything from almost invisable matte to super high gloss), and as you listed, tung or linseed oil will help as well.