A large share of the Old Testament is story — Joshua, Judges, Samuel, Kings, Chronicles, Ezra, Nehemiah, Esther, and much of the Pentateuch. It isn't quite like anything else we read, and it rewards a particular kind of attention.

What to keep in mind

Enter into the scene of each story. Pay attention to detail, repeated words, imagery, how characters are portrayed, and what the dialogue reveals.
Enter into the situation of the original audience. What were they facing? What would they have heard in this?
Remember the overall story each book is telling. Every story sits inside a larger story.
Each book is meant to be read in the larger context of God's story as a whole.
These stories usually teach truth indirectly, by showing us God acting in real history rather than by stating a principle.
They are real, not fiction, and they are not G-rated. That realism is the point: it shows us how God works in the middle of human brokenness and messiness.
What people do in these stories is not necessarily a good example. Frequently it's the opposite.
Some stories are meant to provoke questions and raise tensions that get addressed more directly elsewhere in the Bible.

One thing to resist

The instinct with a story is to find the moral — to ask what this character did right so we can do it too. Sometimes that works. Often it doesn't, because the person in front of us is behaving badly and the text never says so out loud.

A better first question is: what is God doing here, and what does this show me about him? The application usually follows from that, and it follows more honestly.