How does time travel work on Doctor Who?

The Doctor shows up somewhere in time and space, and there's always a crisis going on that's going to end the world or something. But as Martha Jones said, "The world didn't end in 1599. It just didn't." The Doctor's explanation is that it's like Back to the Future: you go back in time and change something, and it can change the future timeline. But that's not quite right. When the Doctor shows up, the crisis is already in progress. It's not something he did that caused it. How can that be?