Here is part of a tutorial I did for another site. I hope it's helpful.
We are now beginning to inlet the barrel. The photo the breach end of the barrel resting on top of the Breaching shoulder of the stock. It's about to be inlet to the half way point.
I have now inlet the breach end inlet 1/2 way into the wood so the barrel now lays on top of the stock.
At this point the muzzle is clamped down so it can't move. You can offset it to one side or the other to make the center line of the barrel cast off to the side so I can make the gun with cast-off.
This rifle casts to the left, as it's a left hand rifle This line is very important to the final fit of the stock, and should be drawn on with a marker so it won't rub off. It's going to be there until we inlet the butt plate and shape the comb and the butt stock.
A chisel is sharpened all from one side for this cut. You place the flat on the side of the barrel and hold it in place with the thumb. Press only hard enough to keep it flat. If you push hard you will flex the barrel. YOU DON'T WANT TO FLEX THE BARREL SIDE TO SIDE, SO USE VERY LITTLE SIDEWAYS PRESSURE AS YOU DO THIS.
Lightly tap the chisel to make a cut on the top of the stock.
Here I use a 2" wide chisel to deepen the cut.
Here you see the side cuts set in about 1/16" deep. I pencil down them so I can see them better.
I have drawn a cross section of a barrel channel. On a swamped barrel, the muzzle is wider and deeper than the waist of the barrel, and so is the breach end.
If you take 2 swamped barrels and lay them side by side on the floor, and then pinch then togather with your pinky and your thumb, you will see it takes VERY LITTLE to flex them.
When you flex the outside you flex and bend the bore. If you want a swamped barrel to shoot well it's ABSOLUTELY IMPERATIVE that the barrel not flex side to side or up and down when it's fully inlet.
This is how the barrel will be inlet. First i will remove the wood marked "A". The I will make a trench marked "B" These "trenches" are precise in depth so the barrel is also not warped up and down, just like I was careful not to flex it side to side
it has to lay in a manor so that the bore remains straight.
So I measure the side flats with a caliper to the nearest .0001" at increments of about 4" and I divide it by 2 to get the depth. I do the same thing with the barrel itself to get the half diameter at about 3" increments
I have those written measurements on the top of the stock at the points that they relate to the barrel.
Depth of side flats and depth of barrel, both divided in half.
I will then inlet to those depth with my tools and scrapers until I have the barrel to correct depth. I try to hold + or- .002" at every increment. This is the secret to getting a swamped barrel to shoot tiny little groups
Now I am going to inlet the barrel channel. I start by going half the depth of the side flats. You make a shallow channel to the depth of half the height of the side flats. On a swamped barrel such as this one, you go 1/2 the depth of the flat at the waist. Then cross hatch it at about 1/8" increments with a chisel so you can cut paper thing shavings out of it to adjust the depth deeper toward the muzzle and the breach. Keep your chisel like razors! This is "channel A"
You have to get a bit deeper at 4" increments going towards the breach and the muzzle, as you start from the waist. So, to recap, you cut "channel A" full length at the shallowest depth, and then gently deepen it as you cut to it's final depth.
These are my initial cuts to make "channel B" I take the 1/2 diameter of the barrel at the waist of the barrel and make this channel that deep for it's full length. Take pains with this! You want to be very precise and use the side of a file and a scraper to make sure it's the correct depth at ever 3" increment for the full length of the barrel. I do the procedure the same way as I did "Channel A". 1/2 the depth of the barrel at the waist, and then deepen it a bit at a time with files and scraper going towards the muzzle and then towards the breach.
This is the breach end and the roughed out "Channel B"
Now I take a 1/4" chisel and I rough out the "45s" (45 degree angles on the bottom of the octagon barrel channel)
Now I use my "secret" weapons - Gunline Octagon bedding tools. (you can buy then through Brownells)
You have to use these tools to appreciate them. However they are a bit pricey.
For building only a few guns you can do the same work with bent "foot rasps" which you can make out of mild steel and just make your own teeth with a 3 corner fail. They don't work as easily as the Gunline tools, but they will get you through a barrel channel. You just re-sharpen them with the file a few times per gun.
Here you can see the breach end is smoothed out with the gunline tool, and the bottom of the pic you can see the roughed out channel as it was left by the 1/4" chisel
Here you see the use of a steel rule. Any straight non-flexing edge can be used. I lay it along the bottom and the "45s" and see if it will rock. Any rock shows you where the high spots are. You file them down until you have no dips and humps, and you go SLOW so as to not take more than a very few thousandths of an inch in depth so the barrel will not be flexed at all when it's installed.
I now indicate where I will drill a 1/16th hole to make the center of the barrel channel It will be the center of the rod channel later. I will drill it PERPENDICULAR to the top edge of the stock so it comes out in the exact center underneath the barrel, and so it comes out at the "dogleg" where the rod will enter the handrail.
The barrel is coated with inletting black and the fit is checked and small areas are scraped and filed to insure a perfect fit. Now that after the barrel is fitted for good I slab off the waste wood that was on the sides.