First you need the right tools to remove the barrel, barrel vise, BARREL VISE at Brownells
action wrench, ACTION WRENCH at Brownells
then you will need depth micrometer, head space gages, possibly a lathe to shorten or lengthen the barrel tenon, and reamer for the caliber of the barrel.
put barrel into vise, attach action wrench to action, here I add heat to action where barrel screws in I use a heat gun but a hair dryer will work it just takes longer, then wack the action wrench with a rubber mallet to break loose the barrel from the action, unscrew the barrel, use the depth micrometer to measure the length of the tenon, then measure the length of the new barrels tenon, if they are not the same you will have to chuck the new barrel up in the lathe and either remove some of the tenon or add to the thread relief to lengthen it. A few thousandths does make a difference. Once the tenon is taken care of, take the old barrel drop in the go gage and using the depth micrometer measure the hight the go gage sets above the barrel, then do the same with the new barrel, if they are not the same then you will have to rechamber the barrel with the reamer especially if you had to remove anything from the tenon, I would do the reaming by hand after the barrel has been installed to get a perfect head spacing. screw the action on to the barrel and when it is hand tight give it a 1/8 turn more with the action wrench, check head spacing if its right go shoot.
When reaming use lots of cutting oil, clean out chamber before using gages, take it slow when reaming just keep a constant pressure on the reamer and keep turning it while removing it, never reverse the reamer when pulling it out. check the head space often and wipe the reamer clean often, a sharp reamer cuts very fast so again go slow.
Now if you have the lathe I would do a little blue printing while the action is off the barrel as well.