There's very little information in the books you can use to determine their intelligence.
Even if a dragon did something very smart (like attacking Danys enemies and not her friends), you could argue it was just instinct or dumb luck that it acted in such a way.
One thing we know is that the dragons of old were very good at following commands.
Whether laying waste to Harrenhalls stone towers, helping forge Dragon Steel Swords or helping melt the ancient Valyrian roads (that Tyrion guesses were stones melted together.)
At the Kingsmoot of the Ironborn we find out how such specific commands were given to beats:
Euron Greyjoy claims he recovered a magic horn that can bind a dragon to your will.
If this is true it suggests to me, any feats performed by the Valyrian dragons of old can't automatically be attributed to dragon intelligence.
Unless someone has a better example, the most "intelligent" trick
the dragons have performed that can't be attributed to blind luck or instinct is breathing fire on command...
Drakaris!
scifi.stackexchange.com/users/24882/Mikey Mouse
In A Clash of Kings, the warlocks say ""A wilful beast," laughed a handsome young man.
"
shall we teach you the secret speech of dragonkind ?
Come, come."
"
This implies that dragons can speak, which implies a high degree of intelligence.
Perhaps not human level, but certainly higher than animals.
Of course, the Warlocks may have been lying...
but I don't see why as there were a lot of visions Daenerys saw there which have since come true.
scifi.stackexchange.com/users/712/WOPR
There is some evidence that a dragon can bond to a particular person/rider, and that this 'rapport' leads to an instinctive synergy between dragon and rider.
See: The Princess and the Queen, Dany/Drogon.
So, dragons may seem to be intelligent, but most perceived intelligence by dragons can be attributed to these bonds.
Outside a dragonrider bond, they exhibit an intelligence roughly similar to a smart horse or dog (Dany's three), with the cunning of an apex predator (Drogon, Viserion and Rhaegal in Meereen, Sheepstealer, Cannibal).
scifi.stackexchange.com/users/30883/metao
In some mythology, dragons are more intelligent than humans.
We observe in GoT that the dragon destroyed (with its tail) the scorpion device that had injured it and while this may have been at the command of Daenrys, we did not hear her command.
scifi.stackexchange.com/users/63210/Jeff
Dragons smartness and emotional state seems to be very similar to that of a domesticated dog.
They can take orders: Dracarys:
The order for the dragon to breathe fire.
Valahd:
The order for the dragon to fly.
( Note that it appears Emilia Clarke actually says Fly here
but she was meant to say Valahd ) Drogon!
Valahd.
Game of Thrones, Seaosn
5 Episode 9,
"The Dance of Dragons"
We also know that from a related question that dragons share a deep connection with their dragon riders: Dany and Drogon share deep connection.
And the event in the fighting pit is evidence that Drogon has ability to sense when Dany is in peril.
Game of Thrones Season 5, Inside the Episode #9, 6:44
scifi.stackexchange.com/users/58193/TheLethalCarrot
What do we know about the intelligence of dragons? Is it portrayed differently in the books than in Game of Thrones? I’m specifically curious about the perceived/known intelligence of dragons when they were more numerous in the A Song of Ice and Fire world.
How smart are the dragons in Game of Thrones?
scifi.stackexchange.com
<game-of-thrones><a-song-of-ice-and-fire><dragons>
scifi.stackexchange.com/questions/93097
scifi.stackexchange.com/users/45878/UltimateMollusk
Dragons can develop and relationship or a bond with a particular rider and become good at following commands. However, they are said to be instinctive and be as intelligent as a domesticated dog, and cunning as an apex predator. Though there is not much information available on the intelligence of dragons in books, they are known to be as smart as a horse or dog and have been known to be portrayed as being more intelligent than human beings in mythology. Moreover, they can bond easily with humans and can follow commands like Dracarys in Game of Thrones.
There is very little evidence about the intelligence of dragons in books. Whether it is down to a dragon’s instinct or not, they are very good at following commands and can bond well with humans — and are often portrayed as more intelligent than humans in mythology. Dracarys from Game of Thrones is an example of an intelligent dragon. Their level of intelligence can be compared to that of a smart horse or dog. 