You want to take it in two steps, IMHO. First you want to cut the barrel off square. Otherwise a lap will not work the edges equally, and that results in uneven muzzle gas ejection following bullet exit, and that tips the bullet and can spoil accuracy rather dramatically in some cases. A square cut is most easily done in a lathe because the muzzle doesn't need to be centered to get a true 90° cut. You just chuck the muzzle in a 3 jaw chuck and run the parting tool straight in with the cross slide.
If you don't have that available, the next best thing is a piloted square end cutter like
this one. It takes some skill not to let it chatter. Use plenty of oil and cut lightly. Take your time.
If you can't afford that, you will need to true the cut with a file or a scraper. If the barrel has the usual straight military contour, just laying a square against it and filing the high spots it touches until it is even all around will do it. M.L. McPherson has been known to do this at the range, and draw stares, while he shortens a barrel to find a sweet spot.
Another method of squaring a barrel end will get you surprisingly close. Again, this is for a straight contour military barrel. You put a post level on the barrel and clamp it straight up and down. Put a circular bubble level on your file and file very slowly and carefully, keeping level. Walking around the barrel helps even out your errors. Check the post level periodically for shift, and don't forget to plug the barrel with a wad of tissue to keep the filings out.
Once you have a trued end on the barrel, you can lap it. Rather than buy a lap I prefer to make one. You can download instructions in PDF format from
my file repository. If you buy the crown 90° cutter, you can get cutters with other degrees of taper to finish the crown with. I own them but prefer the lap, as it is self-centering.