I am a 13 year old boy, and have been playing DnD since a few weeks after the (horribly CRAPPY) movie came out. I had no idea it even existed before then. What I did was extreemly odd, and the completely incorrect way to go about learning DnD.
Well, my friends and I ran around LARPing for a while, and then noticed actual rules existed. I first bought the Monster Manual, to add flavor to our LARPS. Then the Dungoen Master's Guide, to add finesse. Then the Player's Handbook, becuase I wanted to know what a f****** DC was.
My advice: First, get the Player's Handbook, then the MM, then the DMG. Read the PHB in order, there's a reason why it's IN that order. As one of the few who taught themselves the game, and did not have a mentor, I should know: the format is very helpful, and you should read it page-by-page, in order. By the time you get to some sections, you may already have a pretty good idea of how they work, from explanation of abilities in earlier sections.
READ IT MORE THAN ONCE.
The fluff, or descriptive text, you can just skim. But try to get as familiar as possable with progressions, class tables, Difficutly Classes (DCs) of certain common skill tasks, common opposed skill rolls, damage of common weapons, modifiers for abilities, and the most common of spells (if you want to play a spellcaster).
I myself took 3 months to finish the book . . . It was my first RPG, but by the time I was done, I had it memorized. Give me a progression, number, spell, whatever, I can recite it off the top of my head. This is not uncommon for RPGers, and after a while, you'll be able to do this to. The progressions all follow tight patterns and don't deviate, so it isn't hard. A few common progressions . . .
Low Saves:
start at +0, increase to +1 at level 3, increase by another +1 every 3 levels thereafter.
High Saves:
Start at +2, increase by +1 on every even numbered level.
Low Base Attack:
Start at +0, increase by +1 at every odd numbered level.
Medium Base Attack:
Hard to put into words, but not that complicated in practicality.
High Base Attack:
Start at +1, increase by +1 every level
Just a bit of advice,
-Jeph