Most asteroids have been discovered through optical observations using ground-based telescopes. The first asteroid discoveries were rather serendiptous, with early 19th century astronomers occaisionally finding them while visually looking for other phenomena. With precise measurements of their postitions recorded against the background of (the apparently) fixed stars, astronomers were able to determine asteroid orbits and recognized them as 'planet-like' bodies, similar too though smaller than the larger planets.
From the late 19th century through the mid-20th century, many asteroids were discovered on photographic plates, with their precise positions and orbits being determined again with reference to the background stars on the glass plates. Specially designed measuring engines were built to aid in the precision measurement of newly discovered asteroids and comets.
The early 1970s saw the establishment of the first dedicated astronomical survey for near-Earth asteroids, the Palomar Planet-Crossing Asteroid Survey (PCAS), founded by Eugene Shoemaker and Eleanor Helin. This survey utilized photographic plates and a blink comparator to identify new asteroids and comets. In the 1980's Eugene Shoemaker, along with his wife Carolyn founded the Palomar Asteroid and Comet Survey (PACS). PACS utilized hypersensitized Kodak Tech-Pan 4415 photographic film and a stereoscopic microscope to detect near-Earth asteroids and comets. Precise astrometric positions were measured with the use of a photo-microdensitometer instrument located at Lowell Observatory. The PACS program was very succesful and in 1993 included the astonishing discovery of comet Shoemaker-Levy 9, a comet captured and torn apart by Jupiter's gravity field. In July 1994, the world's ground and space-based telescopes were all pointed towards Jupiter, and the world watched in awe as the numerous broken cometary fragments of SL-9 plumeted one by one into Jupiter, releasing incredible explosions. More on SL-9 available on Comet Shoemaker-Levy Collision with Jupiter.
Despite the succeses of the photographic surveys, by the mid-late 1980's, a revolutionary new technology was being developed for astronomical imaging: the use of digtially-based 'charged-coupled devices' (CCDs). The University of Arizona's SPACEWATCH® program founded by Tom Gehrels and Robert McMillan was the first to begin formal survey's of near-Earth asteroids using CCDs, and throughout the 1980s and early 1990s SPACEWATCH® developed the instrumentation and software techniques that transformed the way near-Earth asteroids are discoved and tracked, essentailly marking the end of the era for photographic surveys. The SPACEWATCH® project enjoyed many 'firsts' including the first NEA dicovered with a CCD, and the first NEA and comet discoved with computer software. Later in the 1990s, projects such as MIT's Lincoln Near-Earth Asteroid Research program (LINEAR) rapidly accelerated the application of CCDs and moving object detection algorithms and increased asteroid discovery rates by 2-3 orders of magnitude over photographic techniques.
Finally, into the early 2000s, the advent of ever-faster computer processors, improved CCD sensors, practically limitless data storage, and continually improving motion detection algorithms saw the rise of surveys such as the University of Arizona's Catalina Sky Survey (CSS), Lowell Observatory Near-Earth Object Search (LONEOS) , JPLs Near-Earth Asteroid Tracking (NEAT) program, and the University of Hawaii's Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) project. Today the CSS and Pan-STARRS projects dominate near-Earth asteroid (NEA) discoveries and are approaching discovery rates of ~2000 new NEAs per year.