How was Gwaihir so well informed ?

[The Might]

Well, firstly, in the summer of 3018, Gandalf asked Radagast to send word among his friends the birds to learn what they could of the Enemy's plans. The Great Eagles flew far and wide and gathered news of the Nazgul and the mustering of Orcs and Wargs and the escape of Gollum from Mirkwood.

Gwaihir was on his way to Isengard - unaware of Saruman's treachery - to bring these news to Gandalf. It was Gandalf's good fortune that this happened.

And as you say he then searched for Gandalf at Galadriel's request and after rescuing him was sent off to look after the Fellowship and returned with the news of Merry and Pippin's capture.


Now to your question - the first important things he learned he had found out due to Radagast's request to find out more about the Enemy's plans. Again, he was not aware of Saruman, but knew where Isengard was, perhaps from earlier errands involving Radagast or maybe just because he liked flying around.

Once he was involved in the War he of course was sent on errands by members of the White Council and perhaps also flew around to find out more out of his own curiosity. After all, he was on the good side and had interest in helping out.

And last but not least, Gwaihir was the lord of the eagles at the time of the War and as such had hundreds of birds as vassals. Imagine how much information would be gathered by such a number.