Help: Writing a story inside a story.

So in a story that I'm currently working, one of my characters will be explaining a story to another character. But I'm kind of sketchy about how an extremely long dialogue is going to look in written format. Can anyone give me some advice on how to write it?

This happens in the novel The Sweetness at the Bottom of the Pie. The way it's handled there is placing a quotation mark at the beginning of every paragraph until the story is over.

“I would call for a volunteer from the audience—a confederate, of course, who had been rehearsed beforehand. I would bring him onstage and explain, in a comic singsong Mandarin voice, that I was about to kill him, to send him off to the Land of the Happy Ancestors. This matter-of-fact announcement never failed to fetch a gasp from the audience, and before they could recover themselves, I would pull a pistol from the folds of my robe, point it at my confederate’s heart, and pull the trigger.
“A starter’s pistol can make a frightful din when it’s fired indoors, and the thing would go off with the most dreadful bang. My assistant would clasp his chest, squeezing in his hand a concealed paper twist of ketchup, which would ooze out horribly between his fingers. Then he would look down at the mess on his chest and gape in disbelief.

The story goes on for quite a while with almost no interruptions. I personally welcomed the change of pace.

Yes -- in dialogue, a new paragraph from the same speaker will have a quotation mark at the beginning, but be sure not to close the preceding paragraph with a mark. The final paragraph is closed as usual.

Thanks for the advice everyone!

Hey, Moalex! I hope I'm not too late.

Sir Arthur Conan Doyle used this loads, seeing as Sherlock Holmes solved most of his crimes without assistance.

The Time Machine and Crewel Lye. Basically the whole novellas were a story told within a story.

Frankenstein. When the monster was recounting his adventures, Mary Shelley used dialogue. It spanned across multiple chapters, if I remember correctly.

I've never favored the technique, because it robs you of any opportunity to insert description, but if you're using it, here's a tip to follow:

Don't break. With normal dialogue, you break so your reader gets a solid sense of what's going on, but if you break with stories-within-stories (whatever you call it), your reader gets irritated. They were just slipping into the beat and suddenly have to readjust to narration again, or another person speaking, and then re-readjust.

So you're telling me to not break the dialogue up, but try to keep it within paragraphs as much as possible?

Ah, sorry. I wasn't clear. Break the paragraphs all you want, as long there's no unexpected piece of narration:

"[Insert long narrative tale]."

He blah blah ... blah blah blah, and then continued his story, blah blah blahhing.

"[Continue long narrative tale.]"