Just wondering how to lap a barrel and what are the benefits

It is supposed to smooth out any blemishes in the barrel. Threre are several kits on the market. Basically it involves shooting grit covered bullets thru your bore or swabbing the bore repeatedly with grit coated patches. You are wearing away the barrel. I THINK it is used by bench shooters to quickly get their barrels "on line". But then, they routinely change barrels every year.
There is a great deal of conversation and opinion as to its relative benefits. I, for one, think its a sour deal. I'd rather wear my barrel out hunting or target shooting than scrubbing. I think a proper break-in and a bit of target practice will achieve the same thing.
But there are others that will tell you its the straight road to Mecca.

I've fire lapped two different rifles, with the same results. It smoothed the bores some, but not enough to solve the quick fouling problem. It also moved the throat forward about .025.

Most quality after factory barrels are hand lapped. Fire lapping seems to be more in-line with factory rifle barrels.

I have lapped one barrel and made it worse.

I have been buying Lothar Walthar barrels that are hand lapped at the factory.

The steel Shilens are not, but all the Shien stainless are, becuse they have to get the copper out from cutting the riflings.

What I will do is work up a sweat with Flitz on a tight patch. The black stuff is steel comming out.

The grit of Flitz is much finer than the factory hand lap, so there is not dammage I can do.

Fire Lapped every rimfire hand & long gun I own and most other handguns.WORSE result was easier to clean bore. Best was significant accuracy improvement in S&W Mod. 19 .357 and Ithaca Saddle Gun .22 mag.
LBT compound on the bullets, NOT NECO.
Recommend you do it. Beartooth Bullets has VERY good info and products.

Mark

My experiences have all been as a result of extremely bad copper foulers.
Fire lapped 2 with a Neco kit. The barrels are much easeyer to clean, and while it did move the throat foward the gun were made far more usable. Particularly a factory 6mm Rem. barrel.
Have also hand-lapped a 338 barrel (use #220 and #400 grit on very tight patches) and really helped the fouling with it also.