If I have a serious complaint about a teacher, how would I go about resolving it on a local and then on a higher level if results aren't...

There might be a couple of approaches that could be
outlined in your essay.  The first step to discuss in your writing might be how it could
be the best for everyone involved if some level of communication is initiated.  This
could result in an email, a note, or even some type of verbal contact that helps to
bring to light that some type of articulation is needed.  If a student has a problem or
concern with a teacher, being able to bring it out in the open is a good first step. 
Writing about this might be a good starting point.  If this is something that cannot be
done or has not borne fruit, then perhaps moving the complaint up the chain of command
might be the next step.  If this involves a prefect or administration official, that
could be another good move.  This might also involve one's parents to help in the
cause.  I think that elaborating on these steps in your writing could help to clearly
identify the steps that one could take in order to bring about successful results to
this problem.