If the sun stopped shining, the surface temperature of the Earth would drop by a factor of two approximately every two months, according to Cornell University imprint website Ask an Astronomer. This means that the temperature would be too cold for humans within a few weeks.
There would likely be some limited bacterial life left on Earth, as some bacteria seem capable of surviving at very cold temperatures in space. However, any other life form would likely die quickly.
On the Huffington Post, Jacqueline Howard points out that if the sun went out, the first most noticeable change would be the absence of light. This would happen after eight minutes and 20 seconds, which is the time it takes sunlight to reach Earth. Without sunlight, photosynthesis would stop, meaning plants would no longer be capable of taking in carbon dioxide and producing life-sustaining oxygen needed by humans and many living things. Photosynthesis performs 99.9 percent of the natural productivity on Earth, and it needs the sun. Furthermore, the Earth would become cold without sunlight, and the average surface temperature would drop below the freezing point. The ocean surfaces would freeze, although some liquid water and marine life on the deep sea floor could possibly remain.