I think Romans 9:10-24 and Ephesians 1:4-12 pretty much nail down predestination and election as biblical concepts. My favorite analogy is Shakespeare and Macbeth. In the story, Macbeth kills the king in order to usurp the throne. In the context of the story, is Macbeth guilty of killing the king? Certainly. He did it. Is Shakespeare guilty of killing the king? No, Shakespeare didn't kill anyone, he's just writing a story. Could Macbeth have done otherwise? No, because that's how Shakespeare wrote the story. In a similar fashion, we are guilty for our sins, not God. But God foreordained everything that happens (and therefore, of course, knows everything that is going to happen). We are responsible for our sin, and God is sovereign over all creation. In the same way as there is a category difference between Shakespeare and Macbeth, there is a category difference between God and us, so that God is not the author of sin, even though He foreordains it to happen.
A lot of the time, this discussion revolves around the concept of free will - a very tired expression if ever there was one. What is it? There are a number of possible definitions.
1. The ability to do whatever you want. In this case, no one has free will. I could want to assassinate the US President all I want (I don't - this is hypothetical), but I'd never be able to get past the sniper on the roof. Or I could want to be an Olympic athlete all I want, but that doesn't mean I can be one. Incidentally, this is a great reason why the "You can be whatever you want" message at graduations is so tiresome and untrue.
2. The ability to please God. This is my favorite definition. In this case, the unsaved person does not have it (because he's spiritually dead), and the saved person (the person regenerated by the Holy Spirit) does have it.
3. The ability to choose God. This is related to the previous one. I mention it because this is what people usually mean by free will. Again, dead people can't do things.