You can figure out whats happening on the field just from what they show on TV. I wrote an answer on quora on how to do this:

What I enjoy in a football game is understanding the strategy thats being carried out and the efficiency of execution on every play. I've broken down a list of positions/schemes/plays to look for below.

The following applies when watching a regular play from scrimmage - ie one that will be either a run or a pass.

_The offense_

1. First pick out the number of tight ends and their position on the offensive line. This will tell you what base formation the offense is "telegraphing" to the defense. 2 or more tight ends implies that the offense is showing "run" unless its the damn Patriots of 2010.

2. Look at where the running backs are - the full back and the half back. This along with the above, will give you an idea of whether the offense is hedging towards a run or a pass. If they are in line, in front of the QB then you can safely assume a pass or trick play.

3. Next the formation of the wide recievers. Are they split, with a slot or are they bunched on one side.

_The defense_

1. Due to camera angles you wont be able to see some of the players on the defense. But its okay because you can workout where they would be (except for how deep they are playing) based on the offensive formation.

2. The rectangular area in front of the offensive line is called "the box". This is where the running back is expected to try to make a run. Count the number of players in the box. A fast way is to group the players in 3s going from bottom edge of the offensive line to the top.

The number of players in the box will tell you what the defense is showing the offense. If the number of players is >=8 then the defense is expecting a run.

Using the following formula, you'll be able to figure out the number of safeties.

Number of safeties = 11 - (the number of players in the box + the number of wider receivers on offense )

_Position of the safeties_

* 2 Safeties

If you've figured out there are two safeties then this implies that the defense is looking to take away big passing plays but give up the middle of the field.
This will usually be a cover-2 formation or a derivative. If you see that a line-backer is cheating towards the safeties then you know its tampa-2.

* 1 Safety

If there's only one single safety then this usually means that the defense is being aggressive, ie they want to blitz, or are showing that they are expecting a run.

_Blitz_

If the number of players on the line of scrimmage for the defense outnumbers the number of players on the offensive and in the vicinity of the QB then this implies the defense is showing a blitz. Picking out the blitzing player is a lot of fun when watching the Jets, Eagles or Ravens play.

Player in motion

On a passing play, most teams will use the player in motion to figure out if the defense is in zone or man coverage. (They are mostly always in zones but do use man coverage to shake things up.)

So as the offensive player in motion moves, watch who covers him. Does he get handed off from one player to another on the defense or does the same defensive player follow him as he moves from one side of the field to the next. If the same player moves to cover the man in motion then it usually implies that the defense is playing a man-coverage. If the man in motion is handed off between players then this usually implies a zone.

Of course there could be special cases in which the defense chooses man/zone depending on which player is in motion at the time of the snap.

_Exercises_

How do you know if your seeing/understanding enough of the action:

1. On regular plays you should be able to see the "hold penalty" at the same time as it happens and before the commentator explains it on TV.

2. You should be able to call some percentage of the plays as you get familiar with understanding the strategy your team plays as well as the play callers idiosyncrasies and the players who get the most attention on the team.

3. Figure out if the defense is in a zone or man coverage. This will take a while because most defenses dont run a scheme which is instantly recognizable.

As you enjoy more aspects of the game, you'll realize the true brilliance of Peyton Manning, the genius of Rex Ryan and you'll be baffled by how precise these NFL plays are.

These are the basics and there is so much more happening on the field. If you have any questions then please ask them here and I'll update this answer.