First, you have Llewelyn Moss (Josh Brolin), a hunter who stumbles upon a scene of mass carnage. When he investigates the scene, he finds a drug deal gone sour and a satchel filled with money. He takes the money, goes home to his wife (Kelly Macdonald), and the two of them run off before whomever the satchel and drugs belong to shows up and starts looking for the goods. Thankfully for Llewelyn's sake, he is apparently a lot smarter than he looks and has a real survivalist instinct.
It isn't long before the unhinged character of Anton Chigurh (Javier Bardem) arrives on the scene because he has been hired by the owners of the money and drugs to take care of the mess. Chigurh is an odd creature, obviously evil to the core, but he has a set of morals and ethics that drive him. When entering little stores, he will approach the clerk, flip a coin and ask them to call it. If they get it right, they get to live, else, well he will take the pneumatic hammer that he carries around to them and teach them not to be so unlucky. If he makes a deal with you, he will hold up his end of the bargain, but you better keep yours as well.
Chigurh quickly picks up the trail of the Mosses and that leg of the chase begins. Next we have Sheriff Ed Bell (Tommy Lee Jones), who has taken an interest in the murders that Chigurh has been leaving (including that of one of his deputies), and eventually the shootout scene where Moss found the money.
Woody Harrelson eventually makes an appearance as another hired gun who is called upon to find Chigurh and determine what is taking so long, but his part is relatively short in the film... short, but important.
Like I said early on, this movie will leave you with an unfinished, WTF, feeling. In fact, it wasn't until I had a conversation with a literature major friend of mine who had also read the book, that I got a better idea as to what exactly was going on. While most of the screen time is about Llewelyn and Chigurh, the story is actually Bell's view on the world and how the criminals of his father's and grandfather's days are different from his, and how society has changed as the years have gone by.
No Country For Old Men is a really good movie. I enjoyed the acting and most of the plot. It wasn't until I got to the end and felt somewhat cheated that I had any ill feelings towards it. But, there is a reason why it won four Oscars including Best Motion Picture of the Year and Best Writing. It is definitely a movie most people should see once, but you will then have to find that friend of yours who is well read and trained to find those hidden meanings in stories like this if you want any kind of satisfying conclusion.