How should one split up the work between two people? Should one write the even-numbered chapters and the other the odd-numbered? Does each person tell the story from the point of view of a different character or write different story-subarcs? In general, how do one organise the work in a team?
I've written a few short stories with friends via email, with each person chipping in a section. It yields some interesting and fun results, but not what you'd call a particularly coherent story.
For an example of how one pair of pros did it, take a look at this interview with Sean Williams and Shane Dix. Basically, they worked on a story outline together, Sean did the first draft, Shane rewrote/edited, and Sean did one last pass.
Getting together for the outlining or vision at the start seems like a really important step. I could see something like odd/even chapters by different writers ending up with a conflict in styles...which might work really well in some cases.
Another option that doesn't seem to have been mentioned, which might work if you are writing multiple-POV-character fiction, is to switch viewpoint characters between chapters and let each writer "own" one or more of the viewpoint characters. As long as you have a reasonably firm outline, this allows each author to work relatively freely, and in such a case the differences in style may actually add to the flavor of the overall story.
This works best if the characters don't partake in each others' activities too much, but with a shared reasonably solid understanding of the characters among all authors and some editing it may very well work well enough even if the characters intermingle.
Viewpoint character switches can get confusing if done wrong, but of the books I've read, I believe the ones that switch viewpoint character at chapter boundaries have all worked well. Of course you may need a solid round of editing at the end to bring everything together and make sure the story is consistent, but that is probably a good idea anyway so all things considered is probably not a huge drawback.
They way my last few collaborations worked was a bit like this, though these were all for short stories. Together we would come up with the story and work out the plot points for the story, the main character beats and the over all plot and events.
After that was all settled one of us would sit down and write the draft (we would trade off of this each story). Then give to the other who would review and clean up the story a bit more. The back and fourth until we were both happy with that, after that it was posted for the online group.
Usually you can tell who did the heavy lifting on the writing as they got top billing.
I think it depends on the people, what they're good at, and who came up with what.
I've been co-writing as a hobby for the last six years, and in the last year started co-writing seriously. My writing partner isn't great with prose, and his characters can be a little flat, but he's got the most amazing ability to grab interesting ideas out of the air, and he has an instinctive ability to throw in really effective plot hooks. I tend to focus heavily on twisting existing elements into complications and intrigue, and I love character development and plot structure.
We'll write the first draft together on google docs, while chatting about the work on Skype. He'll do about two thirds of the brain-storming and solution-fetching. Some characters are 'mine' (he can't write them), some are his, some are shared. I tend to write a few paragraphs where my characters are acting or talking, then he'll do the same, with some liberties for simultaneous action. Sometimes one of us writes a few pages alone. The POV sometimes gets wonky, and there are style changes, and the prose isn't great. The point of this stage is to get a nicely proportioned skeleton in place.
Then I go in for the rewrite, rewrite everything alone, give his characters more depth, fill in scenes I feel need to be in the story, and occasionally cry to my cowriter to get me out of plot-holes. Once I finish, I'll polish excessively until I'm dragged away, and he'll go through the manuscript and pick out prose problems. (Along with a slew of other people making edits.)
This is a self-published venture, so once that's done with I'll use my multimedia degree to lay out the book in InDesign, then convert into HTML with regular expressions for the e-book version. I also paint the covers, though I may step down from that eventually. We split the proceeds unevenly in my favor, with a written contract saying that if our duties shift, we'll renegotiate.