To bend gun stocks, like the butt stock on a SxS or O/U shotgun for change in drop or to give it some cast off or cast on,,the most common method is to use oil,,usually linseed oil.
The wood is soaked and saturated with it at the area of the bend up at the wrist in this case.
Usually by use of simply wrapping rags soaked in the oil around the stock and letting it soak in.
Remember to keep in mind the fire hazzard of oil soaked rags when doing any of this.
The gun is set up in a special jig to hold it all correctly to apply the bend pressure with screw clamps so it can be pushed into position and held there.
The secret if there is any is the heat applied to the oil soaked wood before any pressure is applied.
This generally through the use of simple heat lamps. Some purveyors of the craft have different approaches and techniques but the idea is to heat the wood with the oil in it. That allow the fibers of the wood to slide over and by each other as the wood is bent.
Yes it does work.
Some stocks allow more movement than others. Wood is wood and each piece is a puzzle unto itself.
When the bends are complete to where they are needed to be, the stocker may bend them a bit more as his/her experience may tell them that the stock may relax a bit afterwards and return somewhat. The extra amt tries to allow for that.
Sometimes the stock will stay put and then later return to it's orig set. It's wood,,it does what it wants to do.
The stock is generally left in the jig or cradle for a day or so to cool on it's own and take the new set.
Any of this pretty much ruins the orig finish if there was any but does not damage the wood as far as dents or scrapes if done right.
Steaming is also done but mostly in the cabinet making trade to bend wood in some pretty tight curves. Think boat building too. Those planks are usually steamed and then quickly laid down so they take the set along the hull line.
Steaming won't ruin the wood.It's just water and what ever is in there will evaporate.
Using the stock bending method with linseed oil and heat lamps to soften the wood for bending will leave oil in the wood. Then you have to remove that with whiting powder (slow but efficient), or some simply dunk the grips in acetone.
If you use acetone of lacquer thinner to de-oil wood that was artificially bent using the heat lamp/linseed oil method, don't be surprised if the wood warps right back to it's orig bent shape again,,but not always!.
That's about all I can tell you..