It's possible to share a group with others in Zotero and this is practical if you're going to co-write with someone. See how to create a group and follow the instructions below to share a group with other members.
1. Go to the group you want to share and choose Manage Members.
2. Choose Send More Invitations.
3. Type in the username or e-mail to the members you want to invite and click Invite Members. You have to use the same address that they used when they created a Zotero online account.
4. The invited member will receive an e-mail with a link to the shared group where she has to choose Join to become a member.
Google Docs is a great tool for co-writing and it works very well with Zotero.
It is recommended to use citations from a shared group if there are many co-writers. This makes it easier to get an overview and all participants can edit the references in the Zotero group if needed. Citations from a private library can only be edited by the owner of the library.
Be aware that it's not recommended that multiple users insert and edit citations in the document simultaneously. This can cause problems with the references in the document.
Read more about creating and sharing groups.