Ah, so very new. What kind of guitar did you get?
I think most people when they first pick up a guitar want to try to learn some songs they like, and they spend most of their time just doing that. That's fun, and you should. However, I would recommend doing something systematic in addition. The best thing you can do is to learn how to properly finger the instrument, so you can practice running scales, e.g. That's the way you build dexterity.
When I got my first guitar (in 1994, for my 12th birthday), I learned from Mel Bay Method 1. It is the most classic beginner book, and I think it's still popular. Even if you don't care about learning to read music (or maybe you're already a musician, in which case you're 10 steps ahead of the game), you'll at least learn the fingering of some basic scales, which it's hugely helpful. You'll feel lame plucking away at Mary had a Little Lamb, but you'll learn a lot.
Also, if you have $10 to spare, ultimate guitar tabs is an awesome app. I'm decent at playing by ear, and I still consult it all the time. Not ashamed to admit it!
Good luck, and definitely ask questions!