How does sunset and sunrise occur?

Earth's atmosphere contains a lot of water vapor and impurities, which is the cause of the sun appearing red when it rises and sets. When the sun is overhead, the light goes through a lot less air than when you look at it on the horizon. Red light has a longer wavelength than other colors and can therefore travel farther through the atmosphere. Most of those really pretty orange skies at sunset are unfortunately caused by pollution.
White light coming from the Sun contains all colors of light from red to blue. The molecules in Earth's atmosphere do not scatter much of the red light, but they do scatter a significant amount of blue light. This effect causes the blue sky.

These molecules scattering light also cause the Sun to appear redder than it really is. When the Sun is high in the sky the amount of reddening is small. However the Sun will still appear redder from the ground than from space because the atmosphere scatters some of the blue light.

When the Sun is low in the sky, much more of the blue light coming from the Sun is scattered away from the direct path towards our eyes. Hence the Sun will appear very red when it is low in the sky.

The same thing happens to the Moon. It often appears very red when it is low in the sky for the same reason.

Much of the beauty of red sunsets or sunrises comes not from the red Sun but from the red clouds just above the western or eastern horizon. Red sunlight reflecting off these clouds gives them the same rich red color the Sun has near the horizon. So in a spectacular sunset or sunrise the entire horizon is red.

The effect can increase when the Sun sets or rises over a large city. Pollution particles increase the effect by scattering or absorbing more blue light than red light.

Enjoy your next spectacular red sunrise or sunset and remember that Rayleigh scattering off molecules in Earth's atmosphere causes the effect.

Further Reading:

Knight, R., Physics for Scientists and Engineers, Pearson, 2004.

Simple

No doubt you have seen a sunrise and a sunset. The sky turns red, orange, yellow and even purple because the colored wavelengths of light travel farther through the air (atmosphere).

When the sun is low in the sky, this long journey through the atmosphere means the colors with shorter wavelengths, like blue, have already scattered or bounced off in numerous directions.

Orange sunsets (yellow and red light waves) appear when the air is clean. Sunsets that are the most spectacular occur when red wavelengths reflect off of overhead clouds.
The red and orange colors of sunset and sunrise are a result of scattering. Molecules and particles in the atmosphere alter the direction of light making it appear red, orange, and yellow.
The sun looks reddish at sunrise and sunset but not at noon because of the distance the light is traveling to reach your eye. At sunset and at noon, the light has to travel through more atmosphere before it reaches your eye and more light gets scattered before it reaches you. Since the blue part of the visible light spectrum is the highest frequency, this part of light is scattered first before it can reach you.
A sunset is more red because light is scattered due to the aerosols in the lower atmosphere. Most sunsets are red or orange due to this.