One of us will start writing a couple of chapters. That person will e-mail those chapters to the other person. The second person will read and make suggestions for changes, write a couple more chapters, then e-mail everything back to the first person. Then we both read the story and revise it to make it the best we can. By the time we're finished playing hot-potato, we've both worked on all parts of the book.
Most books have just one author.
Sometimes writing together is easier. We brainstorm together and take turns writing chapters. The titles come from brainstorming. We write down lots of names that we like and pick the one that we think is the most fun. Polka Dots came from something Liza said in the story.