Here is what scientists might believe of what the future of the Earth and the Sun will be like.
0-500 million years in the future - Earth will continue to do its thing. Humans will evolve into dumb blonde idiots that obsess on porn and celebrities than actually saving the planet. There will be ice ages and warm periods, and the effects of global warming might alter climate, but not as intense in the far future of the Sun. Government regulations try to control Co2 emissions and other emissions to prevent altering of the Earth's temperature.
500 million years - humans witness a little bit of a heat wave. The beaches were full but the temperature of the water start to rise. Massive heat waves throughout the globe and the cessation of the seasons. People near the equater move to the poles and try to inhabitat that area and some people start living underground. Exterresterial life move the earthlings out of orbit and earth goes back to normal for about 2 billion years.
2.5 billion years - Extraterrestrial life decide to push earth even farther and move Mars and other planets even farther. The earth begins to warm up again as it did 500 million years and the sun continues to become powerful. Humans escape the earth after the unconfortable heat - oh the cool humans and the rest suffer. Underground cities are created to withstand the heat of the Earth, and humans create artificial food. Humans become moles that live underground and are need utter protection to live outside with temperatures above boiling. The earths oceans begin to steam.
3 billion years - Earth turns into a greenhouse like Venus and earth becomes new Venus. Mars becomes new Earth with water, air, etc. that is needed for life to survive thanks to long term terraforming. Most life on Earth ends, (except for some bacteria, fungi, algae, and cockroaches if they are lucky) but many humans start living on Mars and even start to colinate even Jupiters moon's such as Europa. Earth turns into a cockroach society as cockroaches rule the world as one of the only few living creatures that could survive immensely high temperatures. Even the underground cities will be too hot for most humans to live; even at the poles, while the temperature rises the farther you dig down and the temperature rises the farther you move up so the safe zone gets narrower and narrower. The depths of the oceans are boiled into the sky so you can't even hide in the darkest part of the ocean.
4 billion years - Mars gets too hot and Earth begins to go through the fire stage. The earth will start on fire. The sun becomes a red giant and it engulfs Mercury and Venus. Humans start migrating towards one of Jupiter's moons and possibly Saturn's moon Titan becomes the new home.
5 billion years - Inner solar system eaten up by Sun.
7.6 billion years - Earth is in the suns stomach.
12 billion years - The sun will be dead. A new sun will be born and life would have been on other galaxies.
1 trillion years. Whatever remains of the Sun will be cooled off into a black dwarf which is simply empty space with no star. The Sun will be dead for real.