"Red sky at morning, sailor take warning. Red sky at night, sailor's delight."
This lore does have some truth to it. In the northern hemisphere, weather systems generally move from west to east across the globe. Thus to have red clouds, the sun must shine on the undersides at either sunrise or sunset when the light from the sun passes through a large amount of atmosphere. This results in the scattering of most of the shorter wavelengths of the visible spectrum (purple, blue, green) leaving behind the red end of the spectrum. If the skies are red in the morning, this is because there is clear skies and high pressure to the east, allowing the sun to shine from that direction underneath clouds moving in from the west - typically ahead of a low pressure system bringing a chance for rain. If the skies are red at night, the sunlight is coming in from clear skies to the west, signaling the approach of clear skies, high pressure, and fair weather.
"If birds fly low, then rain we shall know."
This too holds some truth. A drop in air pressure will cause the air to become heavier and make it difficult for birds to fly at higher altitudes. And a drop in pressure signals the approach of a low pressure system, bringing rain to the area. The birds will also fly low to catch bugs (also flying low due to the heavy air) before the storms move in.
"If a circle forms 'round the moon, 'twill rain or snow soon."
A halo/circle around the moon is caused by light being refracted as it passes through ice crystals in high level clouds. These high level clouds are often (but not always) a sign of an advancing low pressure system (the high clouds are typically the left over tops of cumulonimbus clouds that got blown away at high altitudes). While rain or snow may not always follow, the presence of a halo around the moon provides a high probability of wet weather in the near future.
"From twelve 'til two tells what the day will do."
This one has no truth behind it at all. There have been countless occurrences of nice clear weather in the early afternoon giving way to violent thunderstorms during the evening hours. Plus, when you look at it, by noon, half the day is over with - so you already know what it has done!
"Clear moon, Frost soon."
This one does hold some truth. In the fall and spring, a "clear" moon, or clear sky where you can see the moon, allows for perfect radiational cooling (allowing the daytime heat to escape to space). When radiational cooling happens, overnight temperatures will drop quickly, and can lead to the formation of frost if temperatures get cold enough. But obviously, this does not hold true for the summertime when overnight lows rarely dip to the freezing point.
"No weather be ill, if the wind is still."
Calm conditions (usually accompanied by clear skies, but not always) usually indicates the dominance of high pressure over the particular area. Since highs are large areas of sinking air, they discourage the formation of clouds, strong winds, and precipitation. On the other hand, most people have heard of the saying "the calm before the storm" in which conditions, including winds, go calm just before a large thunderstorm moves through. Such a storm would be visible to the west though. One more occasion in which this lore may not hold true: in the winter time, calm air and clear skies may signal the approach or presence of an Arctic high which is typically accompanied by VERY cold air. And it is very difficult to imagine temperatures of -30 to -40 F as pleasant. BRRRRR!
"A cow with its tail to the west makes the weather best, A cow with its tail to the east makes the weather least."
I know this one from being raised on the farm. Cows prefer not to have the wind blowing in their faces... it does not make them very happy! So, as a result, they will typically stand with their backs to the wind. Since west winds typically mean arriving or continuing fair weather (but not always) and east winds signal the approach of arriving or continuing unsettled weather (again, not always), this lore does hold a bit of truth.
