The NFL is by far the most popular, and profitable, professional sports league in the US (except, perhaps the NCAA, but that is a discussion for a completely different venue), and because it is both popular and profitable, it can do two things with every kind of mass media, force competing media outlets to bid for the right to carry the games, and limit access to their products.
The most sought after product is their live games. If you happen to have a favorite team in your local media market, catching all the games on radio or television is easy since just about every game will be broadcast in the local market. However, if your favorite team is outside of the local market, you may only have a few opportunities to see or hear them on free broadcast media.
Of course, you can always pay for the privilege of watching them play by paying for premium cable channels like ESPN and NFL Network on cable, or for even more high priced options like NFL Sunday Ticket or NFL Red Zone.
Best smartphone option - Twitter plus sports.yahoo.com
However, if you are desperate, cheap, or broke, there are a few free options you can try that will give you at least some of the flavor of a live broadcast. If all you have is your smartphone, go to Twitter just before kickoff and find the hashtag that will work best for your team. Usually the team nickname is the easiest to use, and is much better than the city name. For example, if you are a Dallas fan, #cowboys probably works best, and #dallascowboys may also do it for you.
If you are a stats freak, you can bounce between Twitter and Yahoo, specifically sports.yahoo.com. They post updated stats from all the live games, though your Twitter stream will probably be updated more quickly than Yahoo.
On a laptop or desktop? Look for an online radio station too
Most teams have a live radio broadcast of their games that you may be able to catch online. The team's web site typically has a list of the radio stations that carry the game live. Most radio stations have online audio streaming, though some may block the stream for NFL broadcasts, especially stations in larger cities. You will often have better luck with stations in smaller towns far away from big cities. Just keep trying stations until you find one that works.
You probably only want to try this option on a laptop or desktop for several reasons. The biggest one is convenience. On a regular sized display, you can probably open two or three windows at once, or at least toggle back and forth between windows or tabs, as you check Twitter and Yahoo while listening to the radio station. Also, the radio stations typically have popups for their streaming options, and many smartphone browsers just can't handle that.