How do US elections work?

On the surface, the system for electing US presidents is fairly straightforward. Unlike some countries, Americans vote directly for the leader they want (rather than voting for local representatives or parties in a parliament, who then elect their own leader), with only two major parties to choose from - so on November 6, voters will be making a direct choice between Barack Obama and Mitt Romney’s names on the ballot.

But of course, it's not quite that simple...