How could you discover a planet without seeing it with a telescope?
This usually refers to planets discovered around stars other than the sun. None have been acually "seen" so far. Their presence can be inferred from period shifts in the velocity of the central star (from a Doppler shift of the frequency of prominent spectral lines) or dips in light output when the planet blocks part of the star.
Hundreds of planets of other stars have been discovered this way in the last thirty years. As better telescopes are developed for blocking out the light of the central star, actual imaging of the plantes may become possible in some cases.