Dany Roth did a good job producing an article that is about much more than just Star Trek, but used Axanar as one of the more complicated examples of the (non) interaction between fan and licensed works. It gave a good overview of the copyright-able and non-copyright-able aspects of fan fiction. After what seemed like a decent primer on copyright law, goes into actual lawsuits.
The article also goes into where the courts do not agree amongst themselves with the interpretation of 'fair use' and how that really makes things confusing, and since that can determine the fate of your fan work, it is a crucial area.
The example court cases are very interesting and well worth a read.