Search techniques.
No other planets have ever been seen directly, and direct imaging is very difficult owing to the brightness of any system's star compared with a planet.
Similarly finding some spectroscopic signature, such as atmospheric auroral lines, is very difficult.
Radial velocity searches can be done with high precision so very low amplitude variations (velocities on the order of a few meters per second in stars tens of light years away!) arising from orbital perturbations may be detected. The recent finding of a four day periodicity in data for the solar type star 51 Pegasi is an exciting success, and the best such case yet, but the object is of unknown mass (maybe Jupiter sized) and very close to the parent star at about a tenth of the Mercury-Sun distance. There are other hints of a longer period in the radial velocity data so this may be a planetary system.
Positional astronomy (astrometry) also may detect small wobbles in a stellar path owing to gravitationl influnce of one or more planets. The historically best case, Barnard's star, where observations from the Sproul Observatory were alledged to indicate the presence of two bodies, one of Jupiter's size and one Saturn-size, are almost certainly wrong. The disturbance in the Barnard's star data can be traced to very small instrumental effects. An initial study contained an imaging discontinuity owing to a change in the telescope objective`s mounting cell, and a switch to a different kind of photographic plate with slightly different color sensitivity. Both instrumental and planetary effects are very delicate and happen at the 0.001 mm (0.02 arcsec) level and below. Later work suggests a very marginal detection of one or more objects, but these have never been confirmed by other observatories.
Observations with the Hubble Space Telescope have suggested a small companion to Proxima Centauri, but this remains uncertain.
A set of objects have been inferred orbiting a pulsar (PSR1257+12, Wolszcan & Frail, 1992, Nature, 355, 145), and these may be objects with masses similar to the earth, but they are unlikely to be anything like planets we know. Pulsars are thought to form in the aftermath of a supernova explosion, and any 'normal' planets would likely be obliterated in such a stellar catastrophe.