It is easy to see that the sky is blue.
Have you ever wondered why? A lot of other smart people have, too. And it took a long time to figure it out!
Let’s compose the puzzle starting from the atmosphere. The atmosphere is the mixture of gas molecules and other materials surrounding the earth. It is made mostly of the gases nitrogen (78%), and oxygen (21%). Argon gas and water (in the form of vapor, droplets and ice crystals) are the next most common things. There are also small amounts of other gases, plus many small solid particles, like dust, soot and ashes, pollen, and salt from the oceans.
It is with all this stuff that the light coming from the sun interacts before reaching the Earth’s surface. Well, let’s concentrate a little bit on light then!
Light is a kind of energy that radiates, or travels, in waves. Many different kinds of energy travel in waves. For example, sound is a wave of vibrating air. Light is a wave of vibrating electric and magnetic fields. 
The energy of the radiation depends on its wavelength (and frequency), which is the distance between the tops (crests) of the waves. The longer the wavelength of the light the less energy it contains.
There are plenty of different “kinds of light” (infrared, visible, ultraviolet..), depending on wavelength, and all of them compose the so called electromagnetic spectrum. In particular visible light is the part of the electromagnetic spectrum that our eyes can see. Light from the sun or a light bulb may look white, but it is actually a combination of many colors. We can see the different colors of the spectrum by splitting it with a prism.
Light travels through space in a straight line as long as nothing disturbs it. As it moves through the atmosphere, it continues to go straight until it bumps into a bit of dust or a gas molecule. Then what happens to the light depends on its wavelength and the size of the thing it hits.
Dust particles and water droplets are much larger than the wavelength of visible light. When it hits these large particles, it gets reflected, or bounced off, in different directions.
Gas molecules are smaller than the wavelength of visible light. If it bumps into them, it acts differently. When an electromagnetic wave hits a gas molecule, some of it may get absorbed. After a while, 
the molecule releases the light in a different direction. All of the colors can be absorbed. But the lowest wavelengths (blues) are absorbed and released more often than the lower ones (reds). We say that blue light is more scattered than red light.
As light moves through the atmosphere, most of the longer wavelengths pass straight through. Little of the red, orange and yellow light is affected by the air.
However, much of the shorter wavelength waves is absorbed by the gas molecules. The absorbed blue light is then scattered in different directions. It gets scattered all around the sky. Whichever direction you look, some of this scattered blue light reaches you. Since you see the blue light from everywhere overhead, the sky looks blue!
