I have not read the books, but in the TV series Daenerys's dragons are very small and don't seem to grow. I was wondering how long it will take them to grow to the size that they can be used in battle? Is this mentioned in the books? Will they be of any use in battle for Daenerys or are they merely "diplomatic" tools?
The whole answer is a spoiler if you haven't read all of the last (so far) book, A Dance With Dragons:
I can't find a reference right now to the exact timing, but her dragons are about two years old at the end of the last book, and Drogon (the largest, black and red) is large enough for Daenerys to ride on his back.
Whitebeard tells Daenerys:
Balerion the Black Dread was two hundred years old when he died ... He was so large he could swallow an aurochs whole. A dragon never stops growing, your Grace, so long as he has food and freedom.
When Daenerys asks about freedom, he goes on:
... it was noted that none of the [Dragonpit] dragons ever reached the size of their ancestors. The maesters say it was because of the walls around them, and the great dome above their heads.
So presumably, in the wild, for a dragon to keep growing, it needs to find food and a progressively larger series of caves.
Dragons do not grow to a final size, though males tend to be more muscular then females. Dragons never TRULY stop growing. As long as the dragon lives, it will grow.
There is a sort of prequel book, it talks about the dragon masters and their dragons. It says as long as the dragons live they never stop growing. In one picture the master looked like a bug on the dragon's back, and the dragon looked to be about twice the size of a very large plane.