If we are talking about the modified 3/8" thread with the flat root I usually just use a set of calipers and measure the pilot at the tip of the pin or try and measure between the threads. The measurement between the threads is not that accurate because your calipers are a little canted. So if I need a real accurate fit I measure the pin between the threads then bore my hole slightly smaller by about 0.005". I then take very small passes, a couple thou at a time until the butt of the cue fits. The best is to build a mock up on some scrap. Once you get the fit you want you can simply measure the bore on your mock up and use that size on your shaft.
If it were any other type of thread the proper way to fit a thread is on the pitch diameter rather than the root and you would use a special thread pitch micrometer to measure it's diameter. Or as Niel said you could use thread wires to measure the pitch.