There is a multitude of information available for refinishing/staining/sealing wood. Frankly there is too much. I'll give the rough-and-ready overview and try to answer any questions.
If you like the wood you can keep it as-is. If you want a trenchgun you'll have some work to do.
Wood is stained (very shallow) and possibly coated. Yours is certainly coated by the look of the pictures, aka shellac.
It is possible to remove the gloss shellac with a stripper (acetone or commercial paint stripper). This is a
bad idea. The solvent will turn that gloss into a bubble-gum sticky mess. And guess what? You'll have to sand to remove the stain anyway.
So get sanding with about 100 grit. Sand through the sealant/shellac/top coat and get to the stain. You will need to sand past the stain to get clean, virgin, white wood. Don't worry, the stain does not penetrate deeply and will sand out rapidly.
So now you've sanded out all the coating, stain, scratches and whatever else. You've left with nice clean unblemished white wood. You need to finish sanding, up to about 180 grit. Sanding very fine will leave a smooth finish that does not take a stain real well. Sanding coursely does the opposite. Your choice.
Done sanding. Blow the wood off with compressed air. At this point you can water pop to increase staining (
not recommended). Soak the wood in warm water for a moment or just bathe with a damp towel. Wait a few minutes and the wood grain will open up to accept stain. Shotgun stocks are fairly porous and take a stain well so I do not recommend water popping.
Hand rub the stain into the wood. Wipe excess off with damp towel. Let dry for minimum 24 hours. Recommend topcoat with spare urethane. Remember that common aerosol urethane is one step less than what is stated. In other words: gloss is actually semi-gloss / satin actually flat, etc. Recommend Semi-gloss for the desirable satin look. Dry for another minimum 24 hours. The smell will always be there.
This stuff takes practice but first-timers can get good results. There are all kinds of methods, tip, tricks.
Most of the time wood will stain the way it wants to and the operator has very little control of the final product. This is a big reason practice may not work. What does great on one piece won't do nuthin for the next piece.
Remember for a deep, dark stain: sand coursely (up to 120 grit). Water pop. Let stain soak in for extended periods.
Not-so-deep stain: sand fine (up to 180 - 220). Do not water pop. Do not let stain soak for long.
Do this for shotgun stocks. They tend to take stain very well.
Confused Yet? Don't worry. End result looks like this.
