The older gunsmithing books will have a description of this. Basically, you need to either cast a lap in your bore over a pilot that screws into a cleaning rod, or you upset a piece of lead wire until you have to wedge it into the bore. Coat with a very fine lapping compound and start pulling it through the bore.
You need to pay special attention to getting the slug to exit the barrel cleanly at either end - and this is where the fire-lapping is better than hand-lapping on a barrel that’s already cut to size and chambered.
Most custom barrels that are hand-lapped are hand-lapped prior to being chambered and crowned. I lop off 1 to 1.5” of the barrel blank at the muzzle end to eliminate any “belling” from the lapping. The chamber reaming eliminates the other end’s belling, so that’s not cut back as far.
How much is a new barrel or are they even sold?