How are astronomers detecting planets around distant stars?

This is without a doubt the most exciting thing to happen in astronomy in a long time. Up until recently, we had no proof that planets orbited other stars. Many people thought that our solar system was unique and that Earth is the only habitable planet in the universe. Boy, were they wrong! Not only do most stars have planets orbiting them, there is proof of many having Earth-like planets orbiting in the habitable zone. This is an orbit that allows the planet to have liquid water on its surface. We've gone from the belief that there were no other planets to where there are more planets than there are stars. That's why science is so exciting!
Planets that orbit distant stars are called exoplanets and the way that they are discovered is absolutely fascinating. The very first method relies on the concept that a planet orbiting a star will cause it to wobble. This wobbling effect is minute, but it can be detected by using spectrometers attached to telescopes. Basically, a planet orbing a star will cause the star's spectra to exhibit a Doppler shift (lines in the spectra shift to the red or blue depending on the direction that the star is moving relative to the observer) that changes as the planet moves around the star. This method is good for detecting Jupiter-sized gas giants orbiting close to a small dwarf star. If the planet is moving in an inclined orbit relative to the observer, the wobble effect is much lower. Another problem is if the star is exhibiting anomalous magnetic disturbances it can affect the results or give a false indication. This method has located many large gas giants orbiting distant tars because it takes a massive planet to cause a detectable wobble in a star.
An adjunct to this idea is to note the period of the star's position in the sky. By measuring the change in position caused by wobbling with time, the planet's mass and distance from the star can be calculated. This method is also more suited to locating gas giants closely orbiting distant dwarf stars.
By far, the most useful method is the use of transit photometry. When a planet obits a star and if it transits the star in line with the observer, the star's luminosity is reduced slightly, and the amount of this reduction in brightness depends upon the size of the planet and its distance from the star. Obviously, the closer the planet is to the star and the larger the planet is, the greater the change in the star's brightness. Basically, the planet eclipses the star, blocking out a tiny portion of its visible light. This method requires a very good telescope in a high mountainous location and perfect viewing conditions. It also has to have the planet cross (transit) the disc of the star relative to the observer. Another requirement is the use of a very precise photometer that is capable of measuring very tiny changes in brightness. Telescopes on Earth were only capable of finding a few planets this way.
This impediment was changed when NASA launched the Kepler Mission space telescope on March 7, 2009. This extremely powerful instrument enabled NASA astronomers to find many (1,103 as of January 2015) exoplanets, including Earth-like planets. This amazing space telescope has a primary mirror 4.6 feet in diameter and it has instrumentation that can measure photometrical observances to a precision of 20 parts per million. Even more important, it was designed to measure the size of exoplanets and even to determine the composition of the exoplanet's atmosphere.
One of the main problems with telling whether an orbiting planet is Earth like as opposed to a large gas giant is to know the actual size of the star. One way that astronomers have determined this is to convert the photometric data from the Kepler space telescope into sound. The raw data scan produces a hiss or rattle, and the frequency of this noise determines the size because this sound is related to how much churning of the star's surface is occurring. The larger the star, the lower the frequency of this hissing or rattling.
Kepler-22b is the first exoplanet that was found to be orbiting a G-class dwarf star like our sun in the habitable zone. This planet is 2.4 times the radius of Earth. Some believe it to be an ocean world, but this has not been verified.
So far the Kepler Mission has found 715 multiplanetary systems, which means that these are stars with more than one planet orbiting them. What this means is that our solar system is not unique and that there are plenty of Earth-like planets out there nearby in our galaxy. This planet discovery era of astronomy is only beginning. Exoplanets have actually been detected from Earth based telescopes by blocking the light from the star so that planets can be seen. This is not easy to do, but it has worked for large gas giants orbiting distant stars. There are plans to launch a spacecraft capable of actually observing exoplanets. That would be wild beyond imagination, but if we can do that, I wonder if aliens out there are looking at us.

Thanks for reading.