To create groups, add members to groups and change the settings of your group, login to Zotero.com.
Once you are added to a group and you have enabled syncing, your group library will appear in Zotero client, the program you download to your computer or laptop.
Items can be dragged into a group from My Library or another group and viewed or edited by other group members, if their permissions allow it.
Note that group libraries are wholly separate from My Library. Any items dragged into them are separate copies and changes to the items will not be reflected in your own copy of the item until you drag it back into My Library.