Collaborating is not something to be taken lightly. I can't even imagine trying to write a story with a virtual stranger, or even an acquaintance. It's too intimate. I've collaborated a couple of times with one person who has been a good friend and beta-reader for years. We know each other's styles, strengths, weaknesses, etc. He knows I like plot, he prefers to focus on character development. Even as in tune as we are, keeping a story moving forward seamlessly is very difficult. We don't collab often.
As for our process, we usually use a shared online document -- usually Google docs. Stories are oulined in advance, and any deviation is discussed at length via online chat. (Something neither of us would bother with if writing individually.) We've collaborated by writing alternating scenes, and also by alternating POV.
It's just plain hard. But it does get easier with time, as most things do.
Another option which I've always enjoyed, and which I'm participating in right now, is a "Shared World" anthology. Basically, a group of writers get together and create a "universe" (of any genre). The universe normally has a metaplot, but not always; sometimes the setting is the only thing that's shared. Then the authors write short stories using characters and storylines of their own choosing. What's fun about this is discussing how to slightly interconnect the stories, if we so choose. For example, having a character from one story pop up in another.
And now I've babbled long enough. Great topic.