Astronomers use several methods to hunt for exoplanets.
Radial Velocity Method
Most exoplanets were discovered using this method. Astronomers look for the effect of the planet's gravity on its parent star. In other words, the planet's gravity pulls on the star and makes it 'wobble'. The star circles around the common centre of mass of the whole star-planet system.>
If we look along the plane of the planet's orbit we see the wobble as the star moving towards and away from us. If we are looking down on the system from above then we see the wobble as an astrometric shift. This means the star does a small circle in the sky, compared to other nearby stars which stay fixed in position.
Astronomers find it much easier to spot the star moving towards and away from us. We can detect this as a change in the wavelength of the light which reaches us. As the star moves towards us, the light bunches up and is shifted to the blue end of the spectrum. As the star moves away from us, the light stretches out and is shifted to the red end of the spectrum. Current technology lets us detect changes of just 1 metre per second. This is the same speed as a fast walking pace!
The more massive the planet, the stronger its gravity. So the effect is more noticeable for massive planets like Jupiter. Jupiter causes the Sun to wobble by up to 12.5 metres per second. So it is no surprise that astronomers have found lots of Jupiter-like planets. Gravity also gets weaker with distance. So the closer a planet is to its star, the bigger effect its gravity will have. This is why many of the first exoplanets discovered were so-called 'hot Jupiters'.
A transit occurs when a planet passes in front of a star. As it does so, it blocks some starlight. Astronomers look for regular dips in the brightness of a star as a large planet passes in front of it. The Liverpool Telescope can hunt for exoplanets using this method.
If the planet is giant and close to the star, this dip in brightness can be as large as 2% of the total brightness of the star. It will also occur every few days. This means it is easier to find planets with short orbital periods using this method. Trying to find a planet which takes tens or hundreds of years to orbit its star would take a long time!
We also need to be looking at the star-planet system in the right orientation to spot it. If we look from above the orbit of the planet, the planet will never pass between us and the star. We know that there are millions of stars in our galaxy. It is thought that around 1% of stars might have a transiting planet, although it is difficult to catch one in the act.
Direct Imaging Method
This method tries to get an actual image of the planet. It relies on the parent star, lighting up the planet so that we can see it. This is more difficult than it may seem.
The star will be thousands of times brighter than the planet. This means the planet is lost in the glare from the star. Imagine trying to spot a candle, while someone is shining a really bright spotlight at you. Also, the vast distances involved mean that telescopes find it hard to resolve (or separate) the star and planet. This is especially difficult if the planet is close to its star.
Astronomers have created instruments which reduce the contrast between the planet and star. They use a physical mask called a "coronagraph", to block out light from the star. They also try to reduce the effects of atmospheric turbulence by using space telescopes.