There are three causes of such an effect, the most straightforward (and common) is simply as a result of the Doppler Effect on two receding bodies. In principle this should be specified as the Doppler Redshift, but in practive often the first term is dropped.

The second way in which photons can be shifted to lower frequencies (ie lower energies) is due to the expnasion of the universe. Hence the term Cosmological Redshift. This effect is relatively small except for photons travelling over large distances (ie travelling for a long time during which the universe expands a noticeable amount).

The third way in which photons can be shifted to lower frequencies (ie lower energies) is due to the work that must to done to overcome (escape) any gravitation field. Hence the term Gravitational Redshift. This effect is relatively small except for photons travelling within strong gravitational fields (ie large mass).

The Velocity (v) is then related to the Redshift (z) by the normal Lorentz transformation of Special Relativity (Time Dilation):

1 + z = Wob/Wre = (1 + v/c) / SQRT{ 1 - (v/c)2 } So in the non-relativitic limit, z approx v/c

This is "simply" the "stretching" of the wavelength of light (decrease in frequency) as it traverses an expanding universe (ie. between its emission in space-time to its detection in space-time). The "stretching" is equal to the fractional increase by which space has expanded in during the photons passage.

It can be shown that for a photon starting at a distance r_o from a mass M, then the Gravitational Redshift experienced after the photon escapes to infinity is given by

1 + z = 1 / SQRT ( 1 - 2 G M / ro c2) So in the Weak field limit z approx (G M / ro c2)