To understand the Bible today, you've got to study it. Our culture, and even modern Christianity, are fairly removed from what the Bible actually says in its complete context. It is full of single verses out of place and ignoring the parts they don't understand or don't agree with.
Make sure you get a good Bible (maybe two translations) with good cross references, and use them frequently. Let your curiousity and interest lead you. Don't be afraid to take notes (important stuff, or questions, or stuff that means something to you personally), or to stop and look things up. Don't be afraid to look things up in a concordance or to dig into the Greek. http://blueletterbible.org is a great resource.
Personally I would suggest as a possible course is to read through Luke and Acts first. Then Matthew, Mark, and John. During all of this, look up almost every cross reference, reading before and after it. Then read the first five books of the Bible. Then I'd go back and do the whole New Testament. Then pick back up with the rest of the Old Testament, going with books that suit what you want to learn about: general instruction, praise, prophecy, etc; while also studying by subject.
P.S. Before you begin , it might be helpful to do a little bit of study on the differences between Greek/Western thought and Hebrew/Eastern thought. You can find a 40 minute teaching on this here: http://www.mgmorrow.com/audio/sermons/RayVanderLaan/RayVanderLaan_RVL-Idaho_01_Intro-EasternWesternMind_2010_37min.mp3