You need the outside diameter of the thread (called the major diameter) plus
the pitch of the thread---the number of threads per inch or the metric distance
from one thread to the next. Also LH or RH, and the thread type. Most standard
threads are 60°. There are also 55°, acme, and other weird stuff.
The major diameter is easy. Micrometer, cheap pair of calipers, whatever.
The pitch is easiest to measure if you have a set of pitch gauges. They look
kind of like a set of feeler gauges, but each blade has a different thread cut into
it. Check with both metric and standard gauges---there is no guarantee that the
thread is metric. It's easier to check pitch on outside threads (barrel) than inside
threads. Find a job shop machinist, or a gunsmith that does lathe work. They
will have thread pitch gauges.
9/16-32 is not an uncommon thread fror flash hiders. It's what FAL's use, but on
them it's a LH thread.