First things first. Read Genesis.
Seriously. It's only by reveling in all of the dirty details and carefully poring over the text that you'll be able to understand the theology—or theologies—of this book. But there are a couple more general things you can keep your eye out for while reading.
Number one, the concept of covenant. In Genesis, the deity (a) chooses people and (b) makes big promises to them—promises of land, success, lots of kids, and divine protection. God's covenant with Israel starts here in Genesis 12, and the rest of the Hebrew Bible is the story of how this topsy-turvy relationship unfolds.
Number two, God's promises do not come to fulfillment very quickly or very easily. It's not magic—heck, even the chosen people struggle through wars, famines, sterility, inter-familial drama, jealousy, crimes, deceit, lusts, passions, and everything else that makes for good TV. Except vampires. No vampires here.
So how do God's plans move forward in spite of (or because of?) the all too human motives, purposes, and ambitions. Just think—Rebekah fulfills God's oracle by advising her son Jacob to commit fraud (25:19-26; 27:1-46). And Joseph more or less says that his brother's crimes, lies, and jealousies are part of God's plan (45:4-8; 50:19-21). Confused? So is everyone.
And hey, isn't that the stuff of theology?—trying to make sense of God through all the muck of humanity.
Can you imagine being the guy who wrote Genesis? No? Good. Because that guy doesn't exist. The stories found in this book were being told to kids over s'mores for centuries before anyone put pen to paper (or scroll) about three millennia ago. For that reason, it's best to think about compilers and editors—all with different concerns and agendas—instead of The Guy Who Wrote Genesis.
Abraham and his family probably lived around the 1800s BCE. To give you some context, that's around the time mammoths became extinct. Pet mammoths—score. But the actual stories of Genesis were not written until much later, over a period of time that may have ranged from 1000-400 BCE (scholars will debate the exact dates until they're blue in the face). At some time near the latter end of this spectrum, the various strands were combined (artfully, if we do say so).
Later on, some very smart folks thought Genesis was important enough to include in the Bible—we'd have to agree—and voilà, we have our favorite family drama.