First a warning, the UV inhibitors manufacturers put in their poly finishes does differ. One of the materials has a greenish tint the other a blueish coloration. Neither is noticeable unless one tries to patch a stock with the wrong one. If the patches stick out like sore thumbs no matter your best efforts, take heart the cause may not be yours and a complete refinish is your only recourse.
We'll treat these finishes almost like automotive finishes. Firstly never used sandpaper courser than 220 and 320 is likely better. Of course the metal work has to be removed as do the sling studs. Butt plates and recoil pads as well as checkering patterns are covered by masking tape. Use the 2 inch as the fewer seams the better. Cover the checkering patterns and use a thumbnail to press the tape into the border of the pattern. A sharp knife is used to cut around the checkering pattern and the excess removed. Surface scratches in the finish only can be simply sanded out useing 220-320 sand paper. Use a small block and spred the sanding over a large area to blend into the surface of the stock. Do not, I repeat, DO NOT cut into the wood... If the ding goes into the wood stop sanding at the woods surface. If you cut into the wood it will be very difficult indeed to match the stain coat you just damaged. A refinish is sure to be in your future. If a ding goes thru the finish and dents the wood we will sand nearly through the surface film of the finish material and using 00 steel wool rub the wound a bit. This will remove any remaining finish and most scratches. All the damages to the wood of the stock will ahve to be trated with stem. A cotton and it must be cotton cloth is soaked in water and squeezed out until it's still very very damp but not dripping. It's not a critical thing but too little water and you'll be less efficient at steaming out these dents. As a heat source I use an old time copper soldering iron but an electric clothes iron(nearly as much the antique as the soldering iron) will also work. We need something that's hot but not too hot, should sizzle water and that will stay that way for a while. It also must be able to apply that heat to a relatively small area at a time. The cotton material is folded several times. The multiple layers will give more moisture and thus steam for us to work with. To much material will not allow the steam to penetrate the wood as it should. This is not a critical thing but you will learn thru experience what works best. With the stock lieing on a flat surface hold the cloth over the ding in the woods surface and apply the iron(heat source). The longer the heat is applied the more steam is applied to the wood. Don't burn the cloth, but leave the heat in place as long as possible. It is acceptable to lift the heat and move a unheated part of the folded cloth over the ding then reapplying the heat source. Steam until the ding is raised... If the damage broke the wood fibers in the stock, a totally invisible repair may not be possible but if a lot of steam is applied the fibers will fill the damage and even sometimes raise the surface of the wood a bit. This will allow us to use a smooth faced hammer or chisel butt to tap (lightly) it down. If all goes well it should be nearly invisible, especially after the finish is applied. When all damage is repaired as best possible we'll restore the finish we removed. Before starting the finishing process wipe the stocks untire surface down with a clean cloth and a bit of clean thinner to remove oil and finger prints. I use a rub on poly finish available at WalMart and elsewhere I'm sure. It matches both finish types well and bonds to either. It is also fairly easy to come by and to work with. I apply the finish with the finger tips and you must aviod trying to get too much on in a single coat. Multiple light coats are best. Allow them to dry and recoat as needed. Usually several coats will be needed to bring back the depth of finish and to level the finishes surface. Read and follow the recoating instructions on the finish can as to how long until you can recoat and how long can you wait between coats. If you must wait too long between coats just steel fur(0000) the spots and go ahead and recoat. When you believe you have enough on to level the finish sand very very lightly with 600-800 grit wet or dry paper on a block. I have just used the steel fur to smooth the new material out. After it's sufficiently dried of course. When the repairs are even and level with the rest of the stocks finish give the entire stock a light going over with 0000 steel wool. This blends the finish and is similar to the color sanding a body shop does when fixing an automotive finish.
Here you have to decide how the finish is to end up. If a really shiny finish is wanted I apply a last coat of poly over the entire stock. This last coat I call a slick coat or shine coat. Use your hands to apply and use the least amount of finish material you can and still cover the entire surface. Be very aware of your finsger prints as they certainly will show if your not cautious. I work from the forearm tip to the butt. Allow to thoroughly dry and inspect carefully for any flaws. Any less smooth areas, finger prints or other flaws must be fixed or they will certainly show up on the finished product.
If a satin(still shiney but not glossy) is wanted after steel wool(0000) is used to blend the stock finish simply put on and buff out several coats of a good paste wax containing carnuba. I use Johnsons paste floor wax.. A note here, after handling the stock and for sure after using steel wool on the finish a wipe down with a clean cloth lightly dampened with paint thinner will remove any oils and allow a nuch better finish..
If anything is unclear or if there are questions please feel free to ask.. I am sometimes very poor at explaining anything. While this srrms difficult it really is not..