It may seem obvious, but NFL.com and the NFL Network (TV) are the best places to get NFL information. ESPN is also a pretty good source. If you are an iPhone user (I also am) ESPN has the "ESPN ScoreCenter" app which allows you to set up your favorite sports and teams and check for scores and updates on the fly.
If you watch Total Access on NFL Network you will get a pretty good rundown on whatever is happening around the league. If you want to learn a little more about X's and O's you could watch NFL Playbook (NFL Network) or NFL Matchup (ESPN).
There are some pretty good columnists you could read also. I like Mark Maske (Washington Post), Peter King (Sports Illustrated) and Adam Schefter (ESPN).
If you have Sirius/XM there is a great show called "Moving the Chains" which is usually hosted by Tim Ryan (former NFL player...no real breakthrough insight there) and Pat Kirwin (former NFL front office exec/Jets GM). Kirwin makes the show interesting because you get real insights into the business side of football.
My favorite team is the Giants since i am from New York City, but if you are starting from zero you might want to follow certain players, coaches or play styles.
There are teams that are fun to watch because they play great offense (New Orleans Saints, Indianapolis Colts, Arizona Cardinals), good defense (Baltimore Ravens, New York Jets, San Diego Chargers) or have amazing history (Pittsburgh Steelers, Green Bay Packers, Dallas Cowboys)
Just jump in. If you just start watching the playoffs you will learn a lot. Most of the teams remaining are really fun to watch so now is a great time to jump in.