The purpose for doing an exegesis is to solve problems which
cannot be resolved by a simple reading of the passage. It
brings rigor to the process to control subjectivity.
Pick a passage based on a problem that you do not initially
Write down the problem.
Read the passage over several times and note all the ways that
you can that any clauses or words could be understood in
more than one way. List those various possible meanings and
shades of meanings.
Consult commentaries to see what kind of issues they discuss.
At this stage you are not interested in their solutions to
the problems; you are merely trying to discover what it is
that people have disagreed upon as to the passage at hand.
Look in enough commentaries to come up with issues; more
technical commentaries are generally better about discussing
issues. Write down the issues that you find.
Discuss the passage with friends. See if there are any
difficult areas that they may not understand. Take special
note of any place where their initial understanding is
different from yours.
Write all these problems down that you hope that your in-depth
study will be able to shed light on. Try to arrange them in
order of importance and to discover any dependencies (i.e.
is the understanding of one problem dependent on one of the
interpretations of another problem).