I am not a gunsmith and I don't do barrels for anyone besides myself. I have been swapping barrels on guns since the 1990s and haven't blown up anything yet. This is how I do it and it works for me.
I only know how to do this with Remington or Stolle receivers so the rest of this is from that perspective. Remove the scope and scope base. Remove the barreled action from the stock. - if you have a Stolle glued into your stock, just keep going, you will be fine. Remove the bolt. I dismount the trigger.
You need a barrel vice. Bob Pastor makes
a really nice one. You want to keep the barrel from spinning in the vice and the vice from scraping the coating or paint off your barrel so think toilet paper tubes. Cut the tube long ways, wrap it around the barrel, slide the barrel and paper tube into the vice and clamp the vice around the tube. I have also used leather and it works too. You may get some scrapes - oh well, maybe one of the actual experts here will know a way to do that perfectly.
You need a torque wrench and an
action wrench (scroll 2/3 of the way to the bottom of the page, there is a picture of Bob's action wrench - $45 and works great). Bob Pastor's action wrench slides into the receiver along the path of the bolt, has a hex on the outer end and a flat that fits between the locking lugs. I also have a Davidson wrench that slides in from the side - that kind does not allow you to use a torque wrench so I don't recommend it.
Carefully insert the action wrench into the receiver. In order to fit the torque wrench onto the action wrench you will need a socket. Put the socket on the TW , put the socket on the hex on the end of the action wrench, the TW should be pointing straight up. With your left hand grab that socket and TW. You will hold that left hand steady to avoid putting any sideways force on the receiver. Put your right hand on the far end of the TW and push to the left until action loosens. Remove the TW from the action wrench, remove the action wrench from the receiver, and twist the action off the barrel with your fingers. Don't lose the recoil lug. Write on the lug "front" and "back". You will thank me later. Loosen the barrel vice, remove the barrel and voila - you have removed your barrel.
This is a good time to inspect your locking lugs, clean out the scope base holes, and generally clean up the receiver.
Installing is the reverse with a couple of tricks. This is how I do it, people who actually know what they are doing probably do it better. First, put some anti-seize on the barrel stub. You don't need much, you don't want it forced out of the scope base holes or squeezing around the recoil lug - a little goes a long way. I usually paint on a little then wipe it around with a paper towel then let the next step distribute it evenly around the stub. My stuff is silvery and I put on enough so the threads look silver colored by they are still sharp.
Next, when I put the barrel into the vice, I put everything together hand tight to make sure that the ejection port is pointing in the right direction. I don't think this makes any real difference - it is just what I do. Then tighten the nuts to secure the barrel.
Now you need a device to orient the recoil lug. Some people install the receiver into the stock and use the indentation in the bedding to orient the recoil lug. In my opinion that is too fussy. If I was shooting BR with these guns, I would probably glue the receiver into the stock and this problem would not exist - never mind. You need a lug alignment tool. I use
this one. Screw the lug alignment tool into the receiver, put the lug into the tool - your execution here will be perfect because you wrote the correct front/back orientation on the lug - and by hand twist the receiver onto the barrel until it is finger tight. Insert the action wrench into the receiver. Set the desired torque on the torque wrench. Attach the torque wrench to the action wrench with the TW pointing up, left hand on the socket, with your right hand pull until you reach your setting. I use a TW that clicks. When it clicks once, I click it 4 more times. I don't make it any tighter. Remove the TW. Remove the action wrench. Remove the lug alignment tool. Reinstall your trigger. Remount your barrelled action into your stock. Reinstall your scope base and scope. Install your bolt. If you want to increase your confidence, check your headspace with headspace gauges. You will have to re-zero. I am frequently surprised and pleased by how little I have to slip turrets when I swap barrels.
When you put the barrel into the barrel vice, get the vice as close as you can to the receiver. The closer the better but anything closer than halfway to the receiver will be good. You can buy plastic
caps that screw on to the barrel stub. Good idea. You can also buy barrel bags to store your huge barrel collection. I think I own 4 or 5.
This technique works with a gun where the barrel is torqued on with a reasonable amount. Some factories install barrels with amazing torque and this process above will probably not work - it might but I wouldn't count on it. I use to work with a gunsmith who had a barrel vice with a 4-foot handle to tighten down on the barrel. Some barrels are like that - think original German Mausers.