As outlined last time, Edwin Hubble realized that galaxies seem to recede from us at a rate proportional to their distance. Hence, if the constant of proportionality is known, the distance can be determined to any galaxy, provided is speed of recession. Fortunately for astronomers, one can measure this recession velocity very accurately by looking at the galaxy's spectrum.
The spectrum, of course, is just the light seen from the galaxy after passing it through a prism, or reflecting it off a grating, to, in effect, produce a rainbow. It turns out that spectra of galaxies show particular features, due to the atomic elements in the galaxy. Hydrogen presents particular features, as do oxygen, carbon, sodium, etc. These features are called "lines" because they are so narrow (with widths less than about 1/10000th of the wavelength itself, in the laboratory). That narrowness allows one to detect even the slightest change in wavelength (redder or bluer) of the light we receive.
As with sound, light experiences a Doppler shift from moving sources (like a train passing by), causing the observed change in wavelength. The effect, at first approximation, has a fractional effect on wavelenght of the order the speed of movement over the speed of light (or sound for the train). Since sound moves at 700 mph, a train moving 70 m.p.h. presents a change of 10% in wavelength, which is a couple of piano notes' worth, easy to distinguish audibly. But for light, which moves at 300,000 km/s, a train moving at 70 m.p.h. merits only a change in wavelength of a part in 10 million, difficult to notice. But galaxies, even in the (relatively) local Universe recede from us at more like 10,000 km/s, a change in wavelength of 3% toward the red, easily detectable in the spectrum of a galaxy. This "redshift" is represented by z and is so common a term in astronomy that it is used interchangeably with distance. But for those terms to be truly interchangeable, you have to know the Hubble constant.
Several critical steps in construction of a more accurate distance ladder have fallen into place within the last decade.
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