How to measure spoke length on the wheel?

There are a bunch of spoke-length calculators online (here's one). This tells you what your spoke length should be, not what it is. You'll need to have exact measurements for the current hub and rim, although the calculator I linked to has a database of measurements you can look up.

Honestly its not a lot of work to take a spoke off and measure it properly. Get several spare spokes, and note down the length for next time.

If you measure a non-drive side spoke off the rear wheel (they're easier to get off, remember the driveside ones are slightly shorter, by about 1~2mm but many rear wheels can get away with the same length.

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Another way is to simply measure the visible length of spoke, and add enough margin for the thread.

If you come up with a spoke too short, then it will lack thread engagement and risk tearing out. A spoke too long will poke through into the tube, and even if you file it flush then a long spoke will have the nipple threads over an unthreaded part of the spoke.

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If you meant width/thickness/diameter, then a micrometer is a good tool assuming your spokes are round. A vernier caliper can be accurate enough with care. Most spokes are 1.8 to 2.0mm, but some have thinner sections in the middle so measure in three places.

If you need bladed spokes then there's a lot more options to match up.