OK, I'm back (good film!). *rubs hands* Right...
Going by the Geneva Stellar Evolution Grids (I gather these are basically 'the standard model' for stellar evolution), our dear old daystar has about 5 billion years left on the clock before it starts turning into a giant. By the time it reaches the end of the main sequence, it'll be about twice as luminous as it is now, and about 40% larger. So Earth is probably going to be toast even by this stage.
Then over the next billion years or so it'll start to burn hydrogen in a shell around its helium core and become a subgiant, going from a G3 IV to end up as a K1 IV. It'll expand to about 2.39 radii, and reach a luminosity of 2.88 Sols.
Eventually the helium core will get so massive that it'll become degenerate, and then over the next 500 million years or so it'll climb up the Red Giant Branch, swelling in size and luminosity as it does so. Around 11.3 billion years into its total lifespan - just before the helium core finally ignites in the "helium flash", the sun will be about 120 times bigger than it is today (radius of about 0.56 AU, so there goes Mercury), and about 1500 times more luminous than today (so there goes Venus and Earth, probably). I'm a little fuzzy on the spectral type/size, but I've labelled it as an M1 II at the end of this stage.
That's not quite it though. Once helium fusion in the core starts, the star will actually rapidly contract and settle down into a stable - but relatively shortlived - helium-burning phase. This will only last for about 100 million years, but the Sun will spend most of its time as a K4 III giant, about 12 times bigger than it is today and about 50 times more luminous.
Eventually though, no more helium can be burned, and the sun won't be massive enough to burn the carbon that remains, and it will instead start alternately burning helium and hydrogen in shells around the inert core. The Sun has now entered the Asymptotic Giant Branch (AGB) - which probably lasts for only a few tens of millions of years - and because the shell-burning causes the star's surface to expand greatly and pulsate, so chances are it'll end up as a Mira-type variable. At the end it'll be an M1 II again, but even bigger than it was at the end of the RGB - it'll be about 160 times larger than it is today (radius 0.74 AU), and over 2500 times more luminous!
After this, it'll shed its outer layers (it's been losing mass ever since the RGB phase, but the mass loss really accelerates in the AGB branch, and it'll end up with only around 70% of its initial mass before the final shedding) and turn into a White Dwarf, which will slowly cool for trillions of years. The sun's total lifespan till WD stage: about 11.45 billion years.
That's how the theory goes anyway.
As for M V dwarfs... I'm a little fuzzy on this, actually. As far as I can understand, they'll take up to
trillions of years to reach the end of their main sequences, but their helium cores will actually grow and grow until the entire star's hydrogen is consumed, leaving behind a "helium dwarf" that will slowly cool off.
. Gah!