I think it works however you want it to work, and however, you and your co-writer work best together. I've never written something with someone else, but I've known co-writers where one does the outlining and ideas, and the other does the actual writing, and I've known co-writers where one writes and then the other edits and adds some more and then the first person edits again and writes some more, it just keeps growing and growing, and I've known people who mostly just treat it like a round-robin. I imagine there are as many ways of co-writing as there are of writing.

So what's the project? Because I've always wanted to try writing something with someone, just to try it. (This is not the best reason to write with someone, I admit.)