Well, just to comfort you guys, the sun is not going to disappear anytime soon. It has enough fuel to keep it running for a couple of billion years. However, let us just say that it did. What will the earth do? What can it do?
At the exact moment that the sun disappeared, we would not know. This is because it takes 8 minutes for the light of the sun to reach us. So, for the first eight minutes of the sun being gone, we would still have light coming from the sun, in a way. Once we do realize that the sun is gone, there would be confusion and mass hysteria across the globe. People would riot against there governments, but what would they be rioting for? The most likely answer for that would be food. Photosynthesis in plants would cease immediately after sun stop hitting their leaves. 99.9% of the productivity on earth, is done by plants. Without the sun, plants would not be able to inhale carbon dioxide, and exhale oxygen. In other words, they would all die. Now, I know what you are thinking. If the plants all die, won't we run out of oxygen? The answer is no. Collectively, all humans on earth breath in 6 trillion kilos of oxygen a year, but our atmosphere contains 1 quintillion ( 1 followed by 18 zeros) kilos of oxygen. So, if you include all the humans and animals on the planet, we will still have enough oxygen to last us thousands of years.
Really, the only problem humans would have, would be the temperature. After 1 week, without the sun, the average surface temperature on the earth would be 32 degrees Fahrenheit, or freezing. Now, these temperatures happen all the time and, us, humans can wear coats. The break down of civil order, panic, hysteria, and looters aside, we would be okay for the first couple of months. However, after the first year on earth without the sun, the average surface temperature on earth will have reached -100 degrees Fahrenheit. The only real option humanity would have would be to move to geothermic locations, like Yosemite, and pitch tents next to the geysers. Now we have to accept the facts, after 2-3 years without the sun, all humanity would have died, and including that, the oceans will have completely frozen over.
Fortunately, ice floats, so there would still be liquid water underneath the surface of the ice. The water at the bottom of the ocean would be warm with super-heated water spewed out of vents coming out of the earth's interior. Extremophiles would survive, like they do now, on chemo synthesis. Using the methane and sulfur coming out of the vents to create energy, these microorganisms would be able to survive for billions of years. So, even without the sun, Earth will still have a little glimmer of life for a very, very long time.
Sources:
http://indianapublicmedia.org/amomentofscience/breathable-oxygen-gas-atmosphere/
http://io9.com/what-would-happen-if-the-sun-just-disappeared-464769645
http://space.about.com/od/astronomybasics/f/sungone.htm
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