Headspace is roughly measured using a set of precisely machined "plugs" or gauges. They are inserted into the chamber of the rifle and the bolt brought into battery (closed). The extractor and op-rod spring are removed from the rifle. There are two types the SAAMI and the NATO. Each have different measurements for the NOGO.
By definition, headspace is the distance between the bolt face and the rear face of the gauge - with the bolt resting firmly against the receiver lugs and the gauge touching the front of the chamber. Basically, it is the wiggle/stretching room inside the chamber for a casing when the round is fired. Too much space could result in damage to the casing or rifle.
Practically speaking, a gauge is inserted into the chamber (no extractor or springs) and the bolt is slowly brought into battery. If it closes, the rifle passes the first test. If it does not close, the chamber is too tight for SAAMI specs. Next a (SAAMI/NATO) NOGO gauge is inserted. Again the bolt should be brought into battery. If the bolt does not close on either guage, relax the chamber is good. If it closes on the SAAMI but not on a NATO - the chamber is NATO spec'd. This is generally ok, but you will have to be cautious of the commercial 308 brass used and you will have to give some consideration to how you reload the casing.
As a footnote, I had an issue with Win SuperX 308 in my Weatherby, it was measurably smaller the other rounds and I had some issues. So it can happen, does not matter if it is a Norky or not.
... then move onto the next stage.
Insert the FIELD gauge. If the bolt does not close on the SAAMI, again use some caution as the chamber is larger than the SAAMI recommendations, but nothing earth shattering. If the bolt closes on either the SAAMI or NATO Field gauge, I would replace the bolt or bring to a 'smith to look at. I would not be shooting too much commercial ammo in it because it is very likely that the oversized chamber could cause a fatigue in the casing (having to stretch too much) causing a rupture or worst.
My Norky bolt closed on a SAAMI NOGO, but not a NATO NOGO. Turned out I was about .002" from the max. The rifle shot like a dream, etc., etc.
