Clyde Tombaugh's search for a trans-Neptunian planet (one with an orbit beyond that of Neptune) was not an easy one. Tombaugh often found himself at the Lowell Observatory struggling with photographic plates containing as many as 400,000 stars. His mission? To painstakingly compare several such plates -- and see whether any of the dots had moved.
[Tombaugh found it -- and dubbed it Pluto.]