Though meteorological experts have a variety of means for determining when a storm's brewing in the sky, there's one very simple method available to every layman on the planet: the sky's getting dark. The base of the clouds floating overhead is an ominous black or gray color, and though that's not always a sure sign that rain's coming it's usually a safe bet.
But why does this happen? Surely clouds don't just get dark as a means of foretelling the doom that comes with bad weather, though prophetically enough that does seem to happen, since extremely dark clouds often bring really bad weather (hurricanes, tornadoes, strong thunderstorms, etc.). What's happening in the troposphere to turn clouds dark?
A satisfactory answer requires looking at the water cycle that forms clouds in the first place. The whole shebang begins when heat from the sun warms up sources of water in a given area - bodies of water, ice, snow, what have you - to a sufficient temperature. This triggers evaporation, the process by which a liquid turns into a gas, and the water changes forms into a water vapor. The warmed air then carries this vapor higher into the atmosphere, reaching the cooler troposphere above. This cool air then begins another process, condensation, which turns the water vapor back into a liquid. The state of this liquid, water or ice, depends on the elevation when condensation kicks in.
Condensation results in the creation of a cloud. So now we have our cloud. What determines how dark the thing will be?
The easy answer, and the one that generally determines whether rain is coming or not, is the amount of moisture floating about in the troposphere. The more water droplets there are, the thicker the cloud is going to be (which also results in the generation of different kinds of clouds). And the thicker the cloud is, the more water droplets there are between the base of the cloud and the sun, the less light is going to get through, hence the near-black to gray coloration. The presence of all this water in the sky will also invariably cause rain, and the more water vapor there is drifting in the sky the more rain you're likely to get, and the darker the clouds will usually be.
This, of course, typically only applies to the bottom of the cloud. If you're in a plane traveling over the clouds, for example, or seeing the storm from a great distance, you'll notice that the top of the clouds are white. This is the result of the ice crystals at the top of the cloud reflecting the light sent down from the sun, an effect that doesn't stretch down to the dense, water-laden bases of the clouds.