Inspiration for this question comes from reading Avigdor Bonchek's "Studying the Torah: A Guide to in-Depth Interpretation". What is unique about this book is the way the author has chosen just a few methods of interpretation and given examples to help highlight the process. I've walked away with a few more 'arrows in my quiver' as I go to learn. But I am looking for more.
This is a very good question and something that should be developed throughout ones life.
Particularly in newer reprints of classics, they are heavily footnoted with both additional explanation and source notations. The books of Rabbi Aryeh Kaplan are a great example. A key to developing tools for exegesis is to learn the notes in addition to the text.
That means go to those actual sources and learn what is being brought. You will quickly see how each author approaches looking at each subject.
The set Torat Menachem Hitvadiyut by the Lubavitcher Rebbe is another excellent source to learn from as are the writings of Rabbi Moshe Chaim Luzzato.
What you will discover is that most of the greats walk down the same or very similar paths.