A red sky at night would presume a clear sky toward the sunset/western sky. Many storms come from the west, so if it's clear to the west, you're doing well.
On the other hand, if you see a red sky in the morning that means your sunrise (east) is clear.
Note the saying doesn't take into account what's going on in the western sky -- the assumption is that rain and clear weather goes in cycles (obviously it was not a sailor from Bremerton or Everett who coined the phrase), so if the clear weather is to your east, then that must mean the rainy weather is coming right behind.
But during sunny stretches, both sides might be clear, which sort of flunks the logic. But that's not very romantic for classic sayings.