The spectral lines are imaged (originally on photographic plates), now on some sort of CCD and captured digitally. Then the shift from dead center measured (in my student days, with a micrometer microscope and microdensitometer, right off the glass plate). This is how Hubble proved the Universe was expanding. It was even possible to determine a star's rotation from the lean of the lines (the line from the approaching limb of the star bent to the blue, the receding limb bent to the red).
The ability to analyze spectra is independent of distance, providing there is enough light to detect. With bigger scopes and better detectors, shorter exposures and higher resolutions are possible, and image processing algorithms can statistically remove the noise and give you an exact profile of the line.
It is really scary how much can be determined with the spectroscope. Next to the telescope, it is the most powerful tool astronomers have, (once you untangle all the effects going on simultaneously), even more so than imaging technology.
Space/Science » in reply to I don't know
High dispersion spectroscopy
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