How would Galadriel know?

[lindil]

Galadriel was able [as were, seemingly, any of the powerful Eldar] to use her mind to search for others [or at least others with similar abilities]. She states this baldly when the fellowship all [minus Gandalf] finally arrives on the royal flet in Caras Galadon.

Gandalf the Grey set out with the Company, but but he did not pass the borders of this land. Now tell us where he is; for I much desired to speak with him again. But I can nopt see him from afar, unless hecomes within the fences of Lorien for a grey mist is about him, and the ways of his feet and his mind are hidden from me.

This specifically describes Osanwe, the ability of Ainur, Elves and especially gifted, powerful or trained mortals to send and receive thoughts to each other.

Explored in fascinating detail in the essay by JRRT Osanwe-Kenta.

See Link above for more on it.