I'd suggest using manifests; Fubar has a
great guide on the basics and how to use them for collaborative mapping, and Tyler has a much more in-depth
general guide which doesn't quite go into collaborative mapping, but is very helpful for wrapping your head around how manifests work exactly. Also, in Frozen's
article on Snowplow, he discusses using instances for collaboration, which are somewhat similar (but not quite as useful for collaboration, IMO) to manifests.
As for sharing, I'd highly suggest using a version control system so you can see who made what changes and easily merge changes (plus, along with manifests, means you can both work on separate parts of the map at the same time, and merge them easily).
GitHub recently gave all users access to creating infinite free private repositories, and is pretty good, so that's what I'd suggest. Hope this helped!