I'm in the same boat, as a Fate newbie myself.  Everything starts to come together well later in the book though.  In fact, at first I found myself hating the layout, wishing things like Aspects were explained in detail first, but for me once I reached that section I really had a "light bulb" moment and the whole system fell into place.

Luminos' summary works well too!  

All in all I find the system deceptively simple.  It's different enough from other role playing games to seem complex but once you get it, it just makes sense.  This game gives me the same tingly excitement that Unknown Armies did, with it's blend of simple yet deep mechanics, clever writing, and fun setting.