How can they find another solar system so far away?
Whole bunch of different ways! One of the first extrasolar planets was discovered around a Pulsar, because the planet disrupts the otherwise precise timing of the light we see from the pulsar. Observing transits is a way of determining extrasolar planets and helping gauge their mass, and observing changes in the spectra coming from the star during such a transit can tell us the makeup of the planet's atmosphere. We can also detect "wobble" from stars that have planets, because like our own sun the barycenter of the planetary orbits is not in the center of the star, this can tell us the general mass of the system in general.
In the same way we can learn about the composition of other stars, through their bright-line spectra.
As a side note and to make it even more "computer related" I rather like a program called "Space Engine" which is possibly best classed as a Software Toy. In addition to being able to see a lot of stuff that we know about (I presume it will be updated for this new system as well!) it will also procedurally generate stars and planets, which is good for taking nifty screenshots.
I put a few into an
Album here. Some from Our solar System, and some from a Galaxy far, far away, but quite recently.