I have discovered over time that I hate screws. No not really the concept, but there are far too fucking models. I started collecting screws to put together for my "workshop" were I repair whatever family, friends, enemies want me to look at. I am not great at it, not even good, but I am who they bring things to, and over time I have learned a bit of skills. (Also I fail, sometimes I break stuff and sometimes I hide…
BoltDepot has some fantastic pages (and printable reference posters) that explain how fasteners are measured and described: https://boltdepot.com/Fastener-Information/Fastener-Basics
Once you've got the terminology, it's pretty straightforward to take the measurements. Thread diameter is easy to do with a $2 plastic vernier caliper (I use mine constantly), or fit into the holes in any screw checker. https://www.amazon.com/Stainlesstown-Bolt-Thread-Gauge-Blue/...
Thread pitch is best done with a thread gauge, which is a fold-out affair sort of like a feeler gauge. I've got an inch/metric combo one like this: https://www.amazon.com/ChgImposs-Imperial-Whitworth-Industri...
And then length is easy to do with the ruler on the side of the screw checker, or the calipers themselves. (Use the jaws for the overall length of a flush-type screw, the step-shoulder part for the length of a cap screw.)
There are also combo gauges, I'm intrigued by this type and I should pick one up to see how I like it: https://www.amazon.com/WEN-ME210G-Imperial-Multi-Gauge-Carry...