* Radial Velocity - just as the gravity of a star effects a planet's orbit, the gravity of a planet also has an impact on the star's. It's just this impact is extremely small. By measuring variations in a star's movement due to the planet's gravity we can both detect the planet and estimate its mass.
* Photometry - when a planet moves in front of a star it reduces both the brightness and spectrum of the light we perceive. By carefully measuring this we can determine not only the size of the planet, but also it's chemical make-up - light from the star travels through the atmosphere of the planet, changing its spectrum in response to the elements present.
There are several other ways we can detect and examine planets, but nearly all of them are based not on observing the planet itself but its impact on much larger, detectable things that surround it. There's a comprehensive list here - https://en.wikipedia.org/wiki/Methods_of_detecting_exoplanet...
Not sure what the primary means of doing that is, but I think it includes Doppler shift measurements of the star's light.
Here's a great explanation of the physics involved: http://www.askamathematician.com/2013/04/q-what-kind-of-tele....
This page contains the measurements of the planet which might be the subject of the announcement; it gives you an idea of what kinds of metrics drive such an analysis:
http://exoplanetarchive.ipac.caltech.edu/cgi-bin/DisplayOver...
2. Ignore the confidence intervals around those values.
We've had a pair of binoculars up in space for a while, but it was designed to see way further than Pluto. That is why we have always had blurry images.
For example, here's a Hubble photo of Mars: https://milesobrien.files.wordpress.com/2010/08/mars_hubble....