Here's a nice page on the Sun's future:
The Once and Future Sun. Wikipedia has some more stuff on the
future of the Earth
The Sun is now in the middle of its main-sequence existence, and has gradually been getting brighter.
It started off at about 0.7 of its present brightness, and when it leaves the main sequence about 6.3 billion years from now, it will be about 2.21 times brighter than at present.
But about 1.1 billion years from now, it will be about 10% brighter, and that will be enough to allow water vapor to enter the upper atmosphere without freezing out. Solar UV will dissociate it and the resulting hydrogen will evaporate into outer space. That will make the oceans slowly evaporate into outer space, leaving oxygen behind.
A few more billion years, and what remains of the Earth's water will likely produce a runaway greenhouse effect, much like what Venus has.
Plate tectonics will likely grind to a halt around then, from lack of water and less radioactive heat generation in the Earth's interior.
There may still be volcanoes, but they will be giant, super-Hawaiian shield volcanoes like those on Mars.
The Sun will gradually become a red giant, taking about 1.3 billion years since departing the main sequence. Though hydrogen burning will have stopped in its core, it will start in a layer surrounding it. It will expand to Venus's present orbit size, and the Earth will get a surface temperature of about 2000 K. The Sun will blow off something like 28% of its mass in a big solar wind, making the Earth move out to 1.4 times its present orbit size.
At the end of that time, the Sun will start burning helium to carbon and oxygen in its center, which will reorganize its structure, making it shrink and get dimmer, about 10 times its present size and 40 times its present luminosity.
But it will consume its central helium in about 110 million years, expanding to 20 times its present size and 100 times its present luminosity as it does so. Helium burning will start in a shell around the center, making it expand to red gianthood in 20 million years. It will grow to the size of the Earth's present orbit and its luminosity will be about 3000 times its present value.
It will blow off more matter, ending in 4 big pulses. The 4th one will blow off everything but the carbon-oxygen core, which then cools to become a white dwarf. The Earth will be nearly 2 times farther from the Sun than it is now.
The Sun won't explode, and its changes will be so slow that it will be hard to notice over anyone's lifetime. But it will change.