How many book(s) does the TV show have left before it runs out of existing story?
There’s a recap of the season on Wikipedia. If you’re read the books, that will bring you up to speed.
And if you haven’t, they’re about 3/4 of the way through the 3rd book (A Storm of Swords), though the show isn’t tracking the books exactly…and it’s they’ll have to diverge soon, given that the events of books 4 and 5 take place concurrently (each book concerning itself with a specific set of characters). Unless HBO wants to have half their actors sitting out a season or two, they’ll need to combine both books in the same season.
I’m guessing they probably have enough existing material for 3 more seasons, including the ‘current’ one (starting this weekend).
Yeah from now on it may be bits of two or three books. It’s kinda necessary in TV, e.g. book characters don’t age like child actors, or some plot threads need to fit into a season.
Martin has provided the main plot to the GoT people if anything happens to me. I’d imagine they’d flesh out the details on their own.
Just in case, we’ll make sure you’re okay! I didn’t know you guys were so close 
Heh. Oops. Well I’m actually writing the 8th book. It will come out right after Martin releases the last one, so keep you eyes peeled in 2028!
I would guess only two seasons (4 and 5) since a lot of the material in the two last books is superfluous and doesn’t advance the story, hence will likely be cut off in the show.
I also expect season 4 to be rather packed and season 5 to be a bit light on drama.