Shahrazad is the patron of storytellers, and her sister, Dunyazad, of listeners [the first story, at least, is told to her – Shahryar, the King, is a mere eavesdropper – though interested enough to want to know how it ends].
The full version is vast – Burton’s version runs to ten volumes with six supplementary ones containing stories which, while famous [such as Aladdin] do not actually appear in the traditional manuscripts of the 1001 Nights but were imported by earlier translators, such as Galland, from other collections.
It is, therefore, no disgrace to have recourse to abridged editions, such as that of Andrew Lang, who gives a reasonable sense of the boxes within boxes style [characters within a story tell a story, and sometimes characters within that story tell a story – usually to make a point about their situation, to plead for mercy].
When I told these stories over five lunchtimes in school, I simply chose stories I liked that were appropriate for school and broke them up as I chose, and inserted others within them, just as I pleased. I’m sure any Arabian storyteller would have done the same.
I must mention http://www.wollamshram.ca/1001/index.htm, where you will find links to a complete Burton translation, and to many other versions.