I do this every week in my job, you need a vernier, imperial 55 degree and metric/unified 60deg thread gauges and a thread specification chart/booklet.
The diameter of a tap is always slightly less than the nominal thread diameter. Then using a set of thread gauges you can establish the TPI ( teeth per inch) or metric pitch. Take all your measurement furthest from the end of the tap as a first and second tap are tapered.
If you have a lot of old looking taps you will probably find they are BSW or BSF.
Taps marked GAS are ussually BSP parallel.
Remarking taps is almost impossible as the majority are HSS ( high speed steel) with the markings etched on – a Dremmell may work.
If you need anymore I have draws full especially of the older threads