Often using a dial indicator. A rack and pinion converts the linear to rotary motion, and gears magnify the rotary motion:

https://en.wikipedia.org/wiki/Indicator_(distance_amplifying...

tubalcain has a good video showing how they work:

https://www.youtube.com/watch?v=Rp6D3YTx7iU

You can use an optical flat. Interference fringe patterns will tell you how a surface that was cut perfectly flat on a machine becomes bowl shaped when you unmount the part.

https://en.m.wikipedia.org/wiki/Optical_flat