This is a pretty fundamental part of astronomy. Just look at what you can do with Fraunhofer lines (http://en.wikipedia.org/wiki/Fraunhofer_lines). They are an almost steganographic signature written into the elements.
Just to reinforce jgc's point: this object was not "far away" by spectroscopy standards. You can use the same technique for looking at the most distant stars and galaxies in the sky.
When people talk about Hubble (the guy, not the telescope) detecting the expansion of the universe by looking at redshift from distant galaxies, what he was actually looking at were spectral signatures. He saw all the patterns he expected to see from burning stars, but the lines were smeared out. Because he knew the patterns always form a consistent picture of the atomic structure, and he understood the doppler effect, he was able to estimate the distances of those objects quite accurately. Amazing stuff.
Not quite. From the doppler-shifted spectrosocopy lines, we can figure out what speed everything is moving relative to us, but that by itself doesn't tell us anything other than their speed.
Noting that all the doppler shifts of other galaxies are red-shifts tells us that all the galaxies are moving away from us, but it still doesn't tell us whether speed correlates to distance in any way.
Figuring out the distance of galaxies is a different matter entirely, and is done with standard candles[0].
It's from the standard candles that we can measure distance, and only once we know the distance that way can we make a correlation between speed and distance, from which we see that the further away a galaxy is, the faster it is receding.
Only once we have found that there is a speed/distance curve can we estimate the distance to an object based on its doppler shift. We can't get it from the doppler shift alone.
Might be worth mentioning the use of Doppler shift of the known patterns of spectral lines associated with elements to get information about radial velocity of e.g. a star being observed.
Hyperfine splitting of spectral lines in hydrogen gas caused by the interaction between electron and neutron spin allows you to map the hydrogen in our local Galaxy.
As parent post says this is pretty standard astrophysics, just find any reasonable text in your local library. Or just Google 'astronomy .pdf' for a huge range of handbooks and presentations.
Might be worth mentioning the use of doppler shift of the known patterns of spectral lines associated with elements to get information about radial velocity of e.g. a star being observed.
And more generally spectroscopy: http://en.wikipedia.org/wiki/Spectroscopy