The easiest way is with a screw pitch gauge. One of those little thingies that looks like a feeler gauge with teeth.
If it's Metric you'll need to determine the "pitch". That's how FAR a part will travel when turned one revolution. Common pitches are M.5, M.75, M1.0 and M1.25.
If it's English then you'll need to know the TPI or threads per inch. This has nothing to do with travel but rather how many "peaks" or threads there are in 1". Common TPI's are 32, 28, 24,20, 16, 13.
Pen parts are usually Metric. Usually when you measure an outside thread it will be a little smaller than the nominal or actual size. If you measure a threaded part at 12.85mm it's a 13mm.
What you call a "before thread diameter" would be the "Major" diameter on an outside thread and the "Minor" diameter on an inside thread.
In your case, since you have the male part, I would measure it to get your tap size. If you only had the female part you could measure the minor diameter and then add the pitch to get close enough to the correct size. I hope this all didn't cofuse you, it did me!:biggrin: