In season 4 episode 7, Drogon (presumably) is seen attacking a herd of goats; he burns one of the goats and flies off with it. The goatherd then goes to Daenerys and brings the charred bones of one of his goats.
In season 4 episode 10 a man brings what he claims to be the charred remains of his little daughter before Daenerys, after which she decides to lock up Rhaegal and Viserion in the catacombs. (Drogon is roaming somewhere else at that time.)
After that, Rhaegal and Viserion don't go hunting anymore, while Drogon stays away for quite some time. Also, we sometimes see the dragons "execute" and eat traitors and enemies, e.g. after the death of Barristan Selmy (except that Drogon does not eat Randyll and
But what do the dragons eat while on Dragonstone? By the looks of it, there isn't much to hunt for on Dragonstone. Do they go hunting on the main land? Have they learnt to eat what (perhaps) the Dothraki bring to them?