In Braavos, once the dying Maester Aemon concludes that Daenerys is the prince that was promised he tells Samwell Tarly that he should be with her, showing her the way.  When Quaithe tells Danerys she is trying to show her the way, Daenerys assumes the way is part of the cryptic warning Quaithe gave her in Qarth.
In Westeros the word “way” can refer to a route, such as Gorne's Way  or the Stone Way which is another name of the Boneway a major pass in Dorne and also the Wide Way, another name for the Prince's Pass.
A Clash of Kings
Quaithe urges Daenerys to leave Qarth as soon as possible. When Dany asks for a clarification on this warning, Quaithe gives a cryptic answer:
To go north, you must journey south, to reach the west you must go east. To go forward you must go back and to touch the light you must pass beneath the shadow.
In the House of the Undying Daenerys comes upon a great hall with a splendour of wizards, which turn out to be a false vision of the Undying Ones. There, a wizard king tells her they have been awaiting her for a thousand years. The wizard king tells he they sent Dany the comet in order to show her the way. 
A Feast for Crows
A Dance with Dragons
In the Great Pyramid of Meereen, Daenerys has a vision of Quaithe. When Dany asks her what she wants of her Quaithe replies that she wants to show her the way.  Dany tells her that she remembers the way, reciting what the Quaithe told her in Qarth,
I remember the way. I go north to go south, east to go west, back to go forward. And to touch the light I have to pass beneath the shadow.
—the wizard king, to Daenerys Targaryen