why does sky look blue and clouds look white?

The­re is a physical phenomenon called Rayleigh scattering that causes light to scatter when it passes through particles that have a diameter one-tenth that of the wavelength (color) of the light. Sunlight is made up of all different colors of light, but because of the elements in the atmosphere the color blue is scattered much more efficiently than the other colors.
When you look at the sky on a clear day, you can see the sun as a bright disk. The blueness you see everywhere else is all of the atoms in the atmosphere scattering blue light toward you. Because red light, yellow light, green light and the other colors aren't scattered nearly as well, you see the sky­ as blue.
As explained in "Why do we have blue skies", white light from the sun consists of all the colors of the rainbow. Since light travels as waves of different lengths, each color has its very own unique wavelength.
In much the same way as why skies are blue, clouds are white because their water droplets or ice crystals are large enough to scatter the light of the seven wavelengths (red, orange, yellow, green, blue, indigo, and violet), which combine to produce white light. Clouds will appear dark or gray when either they are in another clouds shadow or the top of a cloud casts a shadow upon its own base.
The darkness of a cloud also depends on the background sky. A cloud will look darker when it is surrounded by a bright sky and lighter when it is in front of darker ones. Not always will a dark cloud mean rain.
More often, the reason we experience dark rainy days is because clouds are blocking the sunlight. Some of the whitest, most pure light can be observed when dark clouds "break apart" and sunlight filters through.