Put your Zotero account's username and password into your Zotero preferences.
One person in your group should then create a group library and INVITE the other group members to join the library. Use their email addresses that they used to sign up to Zotero.
Save your references into the group library. When you sync to the Zotero server, the reference you added will be uploaded to the Zotero server. Then when the other group members sync, that reference will show up in the group library folder in their Zotero library.