Romans 9-11 deal with the question of why it is that so many Gentiles had come to believe on Christ when God's people themselves, the Jews, by and large had not. In the older interpretation of Romans--that it was about how to get to heaven--these chapters seemed completely out of place. One scholar even suggested a long time ago that these chapters did not even belong here, that they had been spliced in at an arbitrary place.
But if you have been reading the last few chapters, hopefully you can see that they are completely appropriate here. Romans 1-4 dealt broadly with the fact that Jews, just like Gentiles, were sinners and violators of the Law. All have sinned, Paul said (3:23), both Jew and Gentile, and thus Jews needed Christ's atonement just as Gentiles did. Romans 6-9 deal broadly wih the question of the Jewish Law. What was the purpose of the Law, then, if keeping it did not make a person right with God?
So questions like, "Why has Israel not believed?" or "Has God abandoned his people?" fit perfectly with the things Paul has been discussing thus far in the letter. In Romans 9, Paul's answer is basically, "Who are you to question God? God is God and can do whatever he wants." Of course Paul goes on to answer these questions, so it is unbelieving Jews and Judaizing Christians he has in mind, people who reject that Gentiles can be part of God's people without getting circumcised and converting to Judaism.
His answer to such people is that God is the one who decides who he will have mercy on and who he will not. Paul is not primarily talking about individuals, another important piece of the puzzle here. His logic, especially if taken completely literally, does have implications for individuals. But individual predestination is not what he is discussing. He is discussing God's right to have mercy on the Gentiles if he wants to do so.
"Not all who are descended from Israel are Israel," Paul says (9:6). It is those who have believed who are, those who have pursued a right standing with God through their trust in Christ (9:30-32). It is only a portion of Israel that are truly Israel, a "remnant" (9:27). Meanwhile, Paul says later, while he has grafted some of the natural branches out, he has also grafted some Gentile branches in (9:17).
Paul pushes back strongly on anyone who would question God's judgment in doing such things. "Who are you, O man, to talk back to God?" (9:20). "Shall what is formed say to him who formed it, 'Why did you make me like this?'" (9:20). Clay does not have the right to complain about the way the potter has made it, and if God wants to make some pottery for noble purposes and other pottery for skeet shooting, that is his right as God (9:21-22).
Certainly it is! But it is essential to recognize that Paul is making an extreme point. The tone reminds me of some of the things parents have said to their children when they are acting up. "If you don't stop I'm going to pull this car over and make you walk!" "I'll take your TV and throw it in the trash!" "I brought you into this world, and I can take you out!" They are extreme statements that, thankfully, the vast majority of parents do not actually mean. If they followed through with them, they would go to jail. 
God is certainly in charge. God certainly is the boss. I personally believe that God could command us to sacrifice our children if he wanted to (cf. Gen. 22). The sovereignty of God, his absolute authority, is a key Christian belief. It is also a key Christian belief that God does not act on his freedom in certain ways because of who he is. The heart of the predestination-free will debate is the fact that the logic of Romans 9, when taken straightforwardly, seems to conflict not only logically with the central Christian belief that God is love, but it seems to conflict with both the way Paul operated and with other things the New Testament says. By the end of the chapter, we hope to have sorted out these sorts of tensions as best we can.
 And let's be very clear here, what the predestinarian is suggesting here goes well beyond the outrage we would feel toward someone who took a newborn, tossed it in a trash bin and left it for dead. The double predestinarian is suggesting that God makes certain people fail and then torches them in all eternity because they failed.
Next: God's directive and permissive will