Depends on what you want, and correct me but it seems that you mean study in general. The thing that I found to be most helpful is finding major themes about the bible. I was totally shocked how ignorant about the bible I was, and still am for that matter, because of the WTBTS teachings. I didn't even know much about the new covenant. So, I had to start at the beginning and see why people even classify the Hebrew scriptures as the Old Testament and the Greek as the New Testament. Once getting into specific books I found it helpful to look at several outlines of the book to help me see major themes within the book. This put into context a lot of scriptures that were not used properly by the WTS. I also found it helpful to listen to the bible on audio. Going though it quicker than I could read it gave a new perspective on some of the major themes. I highly recommend doing this, even if you have read the bible several times.
About breaking it down. In seminary there are classes on this very subject, properly called hermeneutics. There are some texts that are a very good introduction to the subject and will force you to grow your biblical study. For all things this is a good principle: find the authors focus (historical setting and context), the text itself ( grammar and lexicon), and interpretation. This principle is probably of little value without fleshing it out, but once understood it is fantastic. The book that I have is Biblical Hermeneutics by Corley, Lemke, and Lovejoy.
Above all the most important thing is to lay aside our thoughts when we enter the bible and pray. This is the hardest thing to do, to read the bible with no notions about what you already believe. Pray that God guides you in your search.
