In the second book of his Inheritence Cycle, Christopher Paolini makes the grievous error of landing his main character in the middle of a serene woodland where he must sit and talk with an old elf for many seemingly unending days. It isn't a true info dump - there are emotions and even some action - but it is still mind-numbingly boring from the expected action, especially compared with the adventurous side story that intersperses it every few chapters.
That being said, this boring section is very necessary. The main character learns many important things, not to mention that he undergoes a vital transformation at that time. Not least of the things learned is how the magic of the world works. This is referred to for the rest of the series.
I now find myself faced with a similar problem. I am developing a fantasy novel of my own, with my own variation of magic. I have successfully managed to explain its inner workings to the reader without info-dumping; but now I have a real problem: it turns out that the protagonist and the reader weren't told the whole picture. There is an entire side of magic - a very important side - that the protagonist must be informed of by the dreaded 'old veteran.'
So far, I have fallen back on the assumption that the 'old veteran' (we'll call him Pete) sits the protagonist down and tells him what he's been missing. Pete does his best to avoid info-dumping. He relates the necessary knowledge in the form of a story, telling how he discovered it. The story is full of action. On top of that, the whole story only lasts for roughly four pages. Despite all this, Pete's tale is still in the form of a narration, and as such, is dangerously close to an info-dump.
Question: In many fantasy novels, there usually comes a point where the magic has to be explained to some extent, so that the rest of the novel can be fully understood. The result of this need is usually an info-dump. How can one relate this necessary information so that the reader does not become bored and fall asleep?
EDIT: This question is similar to this one. However, I feel it is different. While this question deals with a relentless-if-short narration, that question deals with a chapter of inner realization.