The greatest enemy of the night photographer is noise. Even with extremely low ISO settings and the world's steadiest tripod, your beautifully captured sky shots are going to have some unsightly speckles. Now, you could just apply a denoise filter and be done with it, but if you want to retain as much quality as possible, more precise methods exist.
As photographer Dave Morrow explains (both in article and video form), for starry night sky photos, you can "target" the noise better by creating a luminosity mask to prevent your denoise filter of choice (in Morrow's case, it's the free Nik Software Suite) from blurring the bright parts of the shot.
Because there's such a contrast between the light and dark aspects of these types of photos, this method is both fast and effective and doesn't require too much work by hand.
For more details on the settings Morrow uses for the noise filter itself, hit up his blog post on the subject.
Simple & Powerful Noise Reduction for Star, Milky Way & Night Sky Photography [Dave Morrow Photography, via PetaPixel]