How do we discover exoplanets?
Astronomers look for repeatable signals in light, motion and gravity, then test whether a planet is the best explanation.
Transits
A planet passing in front of its star blocks a small fraction of the light. Repeated dips reveal an orbital period; their depth helps estimate radius when the stellar size is known. Blended stars and stellar activity can mimic signals, so confirmation needs additional checks.
Radial velocity
An orbiting planet and its star move around a shared centre of mass. Small shifts in stellar spectral lines reveal motion towards and away from us. Often the result is a minimum mass because the orbital tilt is unknown.
Other approaches
Direct imaging separates the light of a planet from its star, usually for young, large worlds on wide orbits. Microlensing detects the gravitational magnification of a distant background star. Timing measurements can reveal planets through changes in otherwise regular signals.