So the safest place to be if a supernova occurs is very far away from the supernova. A supernova is considered close to the Earth if it's less than 600 trillion miles away from the Earth. Supernovas that are this close and would be a problem for us are estimated to occur about 2 times every billion years. Though this is a rare event, experts think that one of the Earth's big extinctions happened this way about 500 million years ago that killed 60% of all living things in the ocean! What happens is that when a star explodes and becomes a supernova, it produces super energetic light called gamma radiation that breaks down the atmosphere. The atmosphere is like a big blanket that keeps the Earth safe from all of the radiation from space, so if it breaks down, a lot of living things die. If this happened near Earth, the only safe place would be far away from Earth because there would be no safe place to be on the planet anymore. Though if you had to stay on the Earth, you would want to be in a bunker with very thick walls that could block out some of the radiation.

Though realistically, the radiation would kill many of the ocean creatures at the bottom of the food chain so if we didn't die directly from the radiation, we would die from starvation. Although the explosion of a supernova is quick, it leaves behind a cloud that will still emit harmful gamma radiation. So basically, if there were a supernova, there wouldn't really be much you could do unless you could travel to a distant planet.