Well, the way I've normally seen it done, it's done in turns.
For instance:
There are three people in the thread. The one who began it normally goes first, then the second person, and the third, and the process repeats.
In my opinion, it's a bit rude to keep posting different posts up, especially since the other person may not log in as much as you do. (Let's just say that you do post every time you log in.) So when the person gets done with one post, they now have a whole slew they need to answer. And, not only that, it seems to junk up the thread.
If something needs to be added into a post, just edit the post and put a little OOC at the top or bottom that lets the other RPer know what's changed about it so that they can make proper adjustments if need be.
...It's early here (2:21 A.M.), so let me know if that makes sense at all or if I missed anything. ^-^;