Terrestrial planet
There are several ways to detect planets that might exist orbiting other stars.
1. Observe the wobble in a star. If a planet orbits the star then there will be a slight movement in the star's position as the planet's gravity tugs at it. From the amount of observed movement, the ratio of the mass of the two can be inferred.
2. Observe a periodic change in the Doppler shift of the light from the star. This periodic shift would also indicate a wobble caused by an orbiting planet. The shift occur as the star is alternately moving towards the Earth and away from the Earth.
3. Observe a periodic change in the brightness of the star. There will be a slight change in brightness when the planet transits across the face of the star. A detectable change will only occur if the orbital plane of the planet is within, say, 10 degrees of edge on to us. The size of the planet can be inferred by the amount the brightness decreases. For example, an Earth size planet transiting a Sun size star would decrease the brightness by about 0.001%. Detection is only possible by observing many transits and adding up the values over time; after enough time the signal to noise ratio will be high enough for the planet to be detected.