Measurements are taken over a period of time. I assume that all the stars looked at resolve to more than a few pixels wide on the CCD. In that case you can visibly see the planet travel across the star in successive frames.
Other methods? In theory if the star's rotating fast enough and you see it side-on, then roughly half the star's light will be slightly blue-shifted (travelling towards you) and half will be red-shifted (away from you). As the planet crosses the star, it will block light coming from one half of the star, then light from the middle, then from the other half.
If there's a dip in the red-shifted part of the spectrum, in time transitioning to a dip in the blue, then you know the planet is moving against the star's rotation. If the dip is blue to red then you know it's following the star's rotation.
And my university lecturer (mentioned in the article) would be very disappointed that I can't remember the actual method of how it's done.
Yes, I'm pretty sure all the measurements done in these sorts of studies are done using the redshift-blueshift method you mentioned. A rotating star has a "red" half and a "blue" half, and a planet transiting the star will cause first a blueshift then a redshift, or a redshift then a blueshift. I went to a talk on this subject a few months ago and was amazed by how sensitively they can pick this kind of thing up.
I think at that stage there was exactly one planet known in a retrograde orbit, but this new discovery shows that they're relatively common rather than being a one-off occurrence. Neato!
I don't think it challenges existing theories of planetary formation quite as much as is described in the article, since our existing theories of planetary formation are already pretty handwavey. I can easily imagine that a planet with a retrograde orbit could happen just due to collisions between large bodies during the planetary formation stage.
Oh, the other important thing to note is that the images are all "artists' conceptions". (Well, except for the one which shows two people in front of a telescope). Telescopes cannot possibly resolve a planet as a little dark disc in front of a big bright disc, so all these measurements just rely on the slight darkening of the star as the planet passes in front.
You can't actually visibly see the planet travel across the star, however. What you measure is the periodic dip in the number of photons collected by the CCD.
Other methods? In theory if the star's rotating fast enough and you see it side-on, then roughly half the star's light will be slightly blue-shifted (travelling towards you) and half will be red-shifted (away from you). As the planet crosses the star, it will block light coming from one half of the star, then light from the middle, then from the other half.
If there's a dip in the red-shifted part of the spectrum, in time transitioning to a dip in the blue, then you know the planet is moving against the star's rotation. If the dip is blue to red then you know it's following the star's rotation.
And my university lecturer (mentioned in the article) would be very disappointed that I can't remember the actual method of how it's done.