He discovered Pluto in 1930 at Lowell Observatory in Flagstaff, AZ during a systematic search for a trans-Neptune planet (also called Planet X) predicted by Percival Lowell and William H. Pickering. Named after Roman god of the underworld who was able to render himself invisible.
Tombaugh's discovery involved painstaking use of a blink comparator -- a device which allows someone to compare two similar photographs by placing them in the viewer's field of vision, and then letting the user switch back and forth -- blink -- between the two. Tombaugh used the blink comparator to compare photographs of sections of sky taken months apart. A moving object, such as a planet, would appear to jump from one position to another while the more distant objects, such as stars, would appear stationary. Tombaugh noticed such a moving object in his search, and subsequent observations showed it to be the planet we call Pluto.