Our sun, at 4.6 billion years old, is comfortably middle aged at the moment. Scientists predict that it will kick the can in another 5 billion years or so. With any luck, we won't be around when it happens, but let's imagine what it would look like if the sun suddenly bought it today. First things first, if the sun did anything at all, we wouldn't know about it until 8 minutes and 20 seconds later, as that is the length of time it takes for light to travel from the surface of the sun to the Earth.
If the sun simply switched off, obviously we would all be plunged into endless darkness, but we might well stay warm for a bit longer due to the insulating layer of atmosphere that surrounds our planet. That said, it probably still wouldn't be comfortable. Within a week, temperatures would dip to an arctic -20°C, after a year, this dips to -75°C and continues to fall until it hits a stable -240°C. We might be able to stay warm by moving underground, particularly close to a nice warming source of geological activity.
Unfortunately, you won't have long to enjoy your new, volcanic home, as you will starve to death pretty quickly. With the sun gone, plants can't no longer photosynthesize and they die. Next up are the animals that eat the plants, then the animals that eat the animals that eat the plants (that's us). This is just if the sun magically switched off (or inexplicably turned into a black hole), if the sun actually "dies" then things would potentially be a lot worse. A star of our sun's mass is unlikely to explode, but it will probably turn into a red giant.
As the name suggests, this means that it's going to get bigger. So big, in fact, that it will simply swallow the Earth up. The entire planet will vapourise, mixing its material with that of the sun. The last thing you will see is a fiery sky bearing down on you before you disintegrate. Eventually there will be nothing left of our solar system but burnt up ashes and some cold, dead outer planets. So that's cheery.