Percival Lowell wanted to find Planet X. Following the model of the discovery of Neptune by detecting perturbations in Uranus' orbit, Lowell hoped to pinpoint a 9th planet. He spent the tail end of his life hunting without success. He used his family fortune to build an observatory, and his will left funding for it to continue its work after his death.
Tombaugh was brought in to carry on the search. By comparing photographs taken a few days apart, he could watch for moving objects. While looking at a spot Lowell's calculations happened to have predicted, Tombaugh spotted a moving object. It was dimmer than Lowell had predicted, and it turns out Lowell had overlooked it because it was so dim.
It appears that the overlap between the location of Tombaugh's observation and Lowell's prediction may well have been accidental. Lowell predicted that Pluto would be many times larger than it is, and that prediction was what allowed estimation of its location.
Because it's so small and so distant, Pluto has always been a bit mysterious. A month ago, January 19, NASA launched New Horizons, a spacecraft designed to gather data on Pluto, and hopefully Kuiper Belt objects beyond Pluto. It'll arrive at Jupiter in 2007, going closer than the Cassini probe did. Then it'll drift until 2015, gathering space dust in a collector designed by college students.
Once it arrives at Pluto, it'll take various sorts of pictures, measuring the atmosphere, surface and geology of Pluto.
Beyond Pluto lies the rest of the Kuiper Belt. Most astronomers seem to agree that Pluto is a largish Kuiper Belt Object (KBO), as is its moon, Charon. New Horizons will push past Pluto into the poorly understood Kuiper Belt, hopefully allowing us to better understand the relationships between Pluto, the other planets, and the KBOs.
Ain't science grand?