Suppose I have a light wave and I want to measure its amplitude, or check to see if it has an amplitude of a certain value: how would one go about doing this?
Direct measurement of the amplitude of the optical field requires interferometric techniques. One that works is the FROG - Frequency Resolved Optical Grating. There are many variations on it today, including from the original developers: Trebino Research Group.
These devices were designed for ultrafast pulses. For CW one usually just measures intensity and polarization, followed by a computation.