I have purchased a new to me, but used M82a1 and I would like to check headspace. I have the gauges, go-nogo and would like to know the exact procedure for the Barrett rifle.

I ordered a manual but it’s back-ordered and would like to shoot it with peace of mind. I know it’s probably fine but still.... just wanna check

Remove the ejector. Place headspace gauge in chamber. SLOWLY let the bolt/carrier forward. Go gauge will close all the way and leave about an 1/8" gap between the front edge of the carrier and the rear edge of the barrel extension.
No go gauge will save it open quite a bit. About a 1/4" or a shade more.

Reassembling the ejector is a pain in the was.
Best thing to do is cut off a spent cartridge and leave about 3/4" of the base.  Nail or screw The base into a wood work table on the side of the table. Screw it down through the flash hole of the primer pocket.

All our work takes had that set up when I worked there. It was easy as hell to put the ejector in. Make sure the extractor is installed.