How To Study Tanach

As a follow-up to my previous post I would like to elaborate on what I think is the best way to learn Tanach.  I noted in that post that I think that learning Tanach (and again, I really mean Nach because learning Torah in-depth goes without saying and is already part of everyone's standard curriculum, I hope) would address a huge moral lacuna that is currently afflicting Orthodox Judaism.  Learning Talmud gives one a legalistic understanding of Judaism but to appreciate the big picture, to gain a real appreciation of the moral imperatives God wants of us one must learn Tanach.
Now the first stumbling block people usually point to when folks talk about learning Tanach is the idea that the text is so deep that without a really strong reliance on understanding how Chazal read the text there is a real danger of reading the Bible and coming to false conclusions and developing heretical understandings.  There is a legitimate concern that people will bring their own automatic assumptions to the table and read the text with those biases.  And I would agree this is a legitimate concern.
After all, modern readers suffer from this innate bias of assuming that our current secular moral system is the pinnacle of human civilization against which all other moral systems, Torah included, must be judged.  Many people also automatically assume that what they take for granted in terms of understandings of the universe and how it works were known to people living centuries or millenia ago.  Either that or they think that these people were simplistic idiots because of their lack of "modern" knowledge.  Reading the Bible without removing these biases can certainly lead to the wrong conclusions.
I'll illustrate with a famous and often-misunderstood narrative from the Bible - the incident of David HaMelech and BatSheva.  For those who haven't read the original, it goes like this.  One day David HaMelech sees BatSheva, a beautiful woman, bathing and decides that he wants her.  He summons her to the palace and they are intimate together.  There's only two problems - she's married to one of David HaMelech's soldiers, and the king got her pregnant.  So David HaMelech summons her husband, one Uriah, back from the battlefield ostensibly for an update on the military situation and then tells him to go home and spend the night with his wife.  Uriah, out of sense of duty to his comrades (and perhaps because he's a wee bit suspicious) refuses and goes back to the battlefield.  David HaMelech instructs his senior general, Yoav, to leave Uriah exposed on the battlefield whereupon the poor soldier is killed leaving David HaMelech to marry BatSheva.
To say that this scenario is problematic is an understatement.  The Gemara clearly wrestled with this and came up with various explanations to try and bring a less negative light to the story.  We are told, for example, that all of David HaMelech's soldiers left a get with their wives in case they didn't come home to avoid any agunah problems.  We are told that Uriah deserved death because he refused David HaMelech's order to go home to his wife.  And while some of these explanations raise an almost "Oh come on!" reaction a close reading of the text actually does support some of them.  A good peirush will point out that while David HaMelech faces God's wrath for his sins, when those sins are listed in detail adultery is not amongst them.  The text is otherwise complete in listing the misdeeds so why not, unless the Gemara's point about the get is correct?
One thing is clear: reading the text unaided or without a non-expect commentary will lead to superficial and incorrect understandings of the text, something we should always avoid.
However, a different problem develops when one goes too far in the other direction.  Trying to read Tanach only through the lens of Chazal and relying completely on their understanding while ignoring the pshat of the text is dangerous as well.  Yes we need to read Chazal's explanations but the pshat has value as well.  Without Chazal we run the danger of transposing our feelings and thoughts into the Tanach's narratives.  To use my example, we might see David HaMelech as an ancient Bill Clinton and not as the supremely important and pious figure that he is to us.  On the other hand we might see him dressed as a Satmar chasid, long curly peyos swaying as he shockles over his gemara while composing Tehillim and speaking in Yiddish to his courtiers.  Using either approach we would completely miss out on the brilliant, complex personality that produced a king favoured by God who was a scholar, warrior and poet whose exploits and writings would be unmatched in history.
But what of the fear that we will see him as all too human?  While this is often raised I would like to point out that Chazal might just have wanted us to appreciate that aspect of the characters in Tanach.  Recall that the Bible we have today did not evolve by chance but was extensively edited by Chazal.  If we have the text of Yechezkel's prophecies, for example, it is because Chazal decided not to hide them away for all time because of the controversial parts in them.  If we have Koheles' musings on life and death which seem problematic from an emunah point of view it's because Chazal felt we could, with proper study, understand them without devolving into kefirah.  If we know the story of David HaMelech and Batsheva it's because they wanted us to know about it in all its unseemly details.  Were Chazal worried we'd lose our appreciation of David HaMelech's holiness by reading that story then it likely would not have made the finally cut.
Chazal, you see, were far more understanding of how to transmit our history and moral lessons than their most pious defenders give them credit for.  David HaMelech's slip with Batsheva, for example, does not diminish his holiness and greatness.  He erred, as all humans do, but remains on a supremely high level because of everything else he did.  The world is not black and white.  A great man can sin but remain a great man nonetheless.  Chazal knew this, they appreciated that our ancestors were humans, great and holy but human nonetheless and did not try to shield us from this reality by censoring our history.
Therefore it's important to approach the study of Tanach carefully but from this realistic position.  Two basic commentaries can be recommended for introduction to the text.  In English, Judaica Press has a fantastic Nach series (they were 2/5 of the way through Chumash when the Artscroll Stoned Chumash came out and ended their plans) and in Hebrew Mossad HaRav Kook has produced a fantastic commentary, Daat Mikra. 
We are reading the stories of and the words of great people, people to whom God Himself spoke and relayed His messages to mankind.  We learn from their deeds and from their mistakes and even more importantly from how they responded to their mistakes.  We seek out the overarching moral priorities to better learn how to be more moral Jews and human beings.  Used in this way, the study of Tanach becomes essential to understanding how Judaism should work.