How is John's story structured?

The simple answer to this question is:  Nobody knows.


In fact nobody can know because at the time John wrote there was no punctuation or paragraphs or chapter divisions.  The chapter and verse markers which we have in our text are additions from much later; they are helpful for referencing which bit of the text we are referring to, but should otherwise be ignored.  The NIV and many other translations from the last 100 years or so place section headings in the text (usually in italics) but these are not part of the original and should not be read as part of the text; they are useful for looking for passages when we don't know verse references. So, does that mean there is no structure and we just have to read all 25 (or so) pages as if it is one paragraph?  For a start, that is impossible, but it also becomes clear as we read that the content is written in "paragraphs of idea".  

We must acknowledge that we cannot know exactly where one section segues into another; as the text moves from the record of one incident to another, the transitions are usually clear , but not always.  Nevertheless, it is relatively easy to divide the whole text into sections that more or less correspond to events or ideas.

However that still means that we end up with our 25 pages of 'incidents' or 'thoughts', chunks of various lengths which act like a long list with no subdivisions.  Most people who study John end up trying to analyse the whole thing and divide it into bigger sections too; sections which would function like the chapters of a book.  People use different approaches to do this.  
The most common is to divide the text by where Jesus is during the narrated events - Jerusalem or Galilee.  These major sections can then be subdivided.  Three alternative methods take note of the seven miracles recorded by John, the mention of Jewish festivals, or the seven times he records Jesus saying "I am something".

Having said all that, nearly everyone agrees that John 1:1-18 is a section on its own, and most people happily call it "The Prologue".  Which sounds scholarly and Greek, but really just means the word before.  A lot of people also think that John 21 was added later, and shouldn't be considered part of the original structure.  Most people will make some kind of major break at chapter 12 (beginning, middle, or end).


So, what do I think?  How have I approached the question?
The simple answer is true:  Nobody knows.
Any structure we use is a device for our own benefit and must be held lightly.