Go to your Zotero library and click icon for New Library > New Group.
You will be prompted to login to your Zotero account.
Once you have logged in, you will be brought to a page to create your group library. Give it a name and click "Create group".
You can change settings for who can read or edit the group library under "Library settings". You can also invite other members to the group library under "Member settings".
Sync your Zotero Library
Once you have created a free Zotero account, you can sync your library across devices.
Open your Zotero library.
Go to Edit > Preferences.
Click on the "Sync" tab. Enter your Zotero account login details. Click "Set Up Syncing". Press "OK" to save.