New planet displays exotic orbit

Do you know what method was used to detect the planet?
I take it that it cannot be directly observed.
How big do they say the planet is?

The star "wobbles" as the planet makes its orbit due to its gravitational effect upon the star. That combined with luminosity testing (the light from the star gets dimmer when the planet passes between it and us) lets us know its speed as well as its orbit direction, although its direction is hardly measured due to retrograde orbits being extremely rare. How much the light dims and how much the star wobbles lets you do the math on its size and mass.

The planet it twice the size of Jupiter, but not as dense.

Only one planet has been directly imaged, and even then it's just a bright speck. The Kepler telescope hopes to change that, its designed to hunt for planets and is sensitive enough to detect an atmosphere.