First, you must understand that the movie requires a certain amount of knowledge of oil/middle east politics, especially the different ethnicities involved. I hope to clear it up as good as possible, but I'm "inside looking out", so just ask, if you don't get me. :)
Second, you must understand that this is not a classical plot where all ends are 100% interconnected, it's more like several plots that overlap at certain intersections. Keeping that in mind I will first write a summary of each subplot and then a short piece about how everything is connected.
Finally please understand that I'm not a native speaker/writer of English, so please be lenient in your reading. :)
The Pakistani/Terrorist Plot:
This is the part that deals with the immigrant workers (among them a father and his son) that work for the large oil company (Connex). They work in an untitled Emirate (we'll just call it "The Emirate" from now on), but they are Pakistani. Being Pakistani, they don't speak Arabic (very well) and don't have very good chances of employment outside the oil industry (scene where the merchant tells the young guy to learn Arabic).
After Prince Nasir pushes Connex out of the Emirate they are hence unemployed (China will most likely use their own workers) and very low on money. At the "madrassa" (Islamic religious school) the young boys get fed and are taught about Islam (actually just a very finite part of Islam). It is here they also meet "The Egyptian" who slowly convinces the young guys that the oil company is just in The Emirate to exploit its natural resources and the workers. Money might have also played a role in it, you might remember that the father is always talking about the mountains back in his homeland and how much he'd like to be there with his wife (the families of suicide bombers get several thousand dollars in "recompensation" from the rich extremist Arabs that back these operations, mostly Saudis, if I might add).
In the final scene of the movie the young Pakistani and his friend drive the activated missile into a Connex LNG tanker.
Prince Nasir's Plot:
Prince Nasir is the eldest son of the Emir of "The Emirate". He's a clever and educated fellow and wants to advance his country from being merely a rich oil reserve for the western powers to a global player on its own, right to this end he cancels the long running oil contract with Connex in favor of a The Chinese bid. This earns him the enmity of Connex and hence the enmity of policy-makers in Washington.
They decide to kill the Emir and use an out-of-luck, old-school-CIA operative, Bob, to set up an assassination while Nasir visits political friends in Beirut. The assassination plot fails (see Bob's Plot below) and Nasir befriends Bryan Woodman (Matt Damon), a bright and energetic energy analyst who is vigorous in his opinion that the oil nations should stop wasting their money and put it into useful investments (again this puts him at odds with the US, that allegedly (no, I'm not gonna go into that discussion here) wants to keep the oil nations backward).
After the assassination fails the US pressures the old Emir into choosing Nasir's younger brother to be the new Emir. The younger brother being a weak willed sucker for attention that is easily manipulated. Nasir, after being notified of this, organizes a coup d'etat, using his popularity with the Emirate's military. Unfortunately the conspirators have an enemy in their midst who informs the US of the plot and gives away the Prince's position in the car convoy, so that US forces can use a missile to take him out.
Bob Barnes is an aging old school CIA operative who has fallen out of favor with the CIA's leadership (essentially his opinion is too complex, being coloured by actual Middle East experience, for the new CIA leadership being made up of "stay at home analysts"). After eliminating two Iranian operatives in the beginning he is given one more shot at a dirty job to pay his dues, He's sent to kill Prince Nasir in Beirut, where Bob still has some good connections in Hezbollah going back to his time there during the Lebanese civil war (early 80s). The job goes wrong because the assassin he hires has since switched sides and he is working for the Iranians (who are friendly towards Nasir, sharing a common enemy in the US after all). Bob is saved only by the timely intervention of his old Hezbollah friend and goes back to the US. Meanwhile the big shots in Washington grow anxious about the botched operation (assassinating foreign heads of state being forbidden in the US after all) and try to lay the whole blame at Bob's feet (accusing him of going rogue). Bob, being a wily field operative, sees danger coming his way and asks his contacts in the Agency who is trying to ruin him, finding out that it is none other than DC-politico Dean Whiting. He then breaks into Whiting's house and threatens him into letting him off the hook (scene in the road stop restaurant). Bob then realizes (after being on the receiving end of DC dirty politics) that Nasir isn't a bad guy after all and tries to save him, unfortunately coming in a bit too late.
The Connex-Killeen Plot (including Sidney Hewitt's and Bennett Holiday's Plots):
Connex, one of the major US oil companies, takes a major hit at the start of the movie, losing concession of The Emirate's oil fields to the Chinese. Looking to consolidate their position they look to acquiring Killeen Oil, a relatively minor player, who recently won concessions to the rich Tengiz oil fields in Kazakhstan. Sidney Hewitt, the head attorney for Connex hires a young lawyer (Bennet Holiday) to look into the deal in order to ferret out any secrets Killeen might have (he most likely already knows that Killeen won the Tengiz concession by bribing Kazakh officials) and to select a scapegoat to take the fall that Washington demands in order to let the merger pass. On the Emirate front Hewitt meets with Dean Whiting and suggests that the CIA take out Prince Nasir, ostensibly for being a terrorist sympathizer (see Bob's plot). After an arduous search Bennet discovers the bribery in Kazakhstan and reports back to Hewitt that Danny Dalton would be a candidate to take the fall. Speaking to the federal attorney he learns that Dalton's not gonna be enough and thus proceeds to set up his boss, Hewitt, for his involvement in transporting Connex' oil from The Emirate through an Iranian pipeline.
The Big Picture:
So, what is the big picture, the glue that binds everything together? Oil. Thats simple.
The US administration knows that for things to continue as they are, they need to look the other way when major oil corporations do their dirty deals (tie in: the Connex-Killeen plot). They will also have to keep the Arab countries from getting their act together and use their field operatives and other dirty means to stop would-be renewers like Prince Nasir (though in my own humble opinion the Arabs do quite a job of stopping people like that themselves usually). Finally they need the illusion of terrorists threatening the US in order to have a free hand in their dealings with the (in real life) so called "axis of evil".
Please note that I have not always taken the time to reveal my own opinion on matters depicted in the film, so please keep your comments on topic, i.e. please only post questions regarding the plot/summary or corrections concerning the plot (I have only seen the movie once yet and had just a cursory inspection of the script). In other words: I do not endorse the message of Syriana 100% so discussing with me on the grounds of this summary is a moot point.