Hello Mary,

Thank you for your post.

Before going further, could you let us know if you want to share folders in users' mailbox, or in document library of Sharepoint Online?

If you want to share folders in user mailbox, you can use cmdlet Add-MailboxFolderPermission to do it. For more information about cmdlet Set-MailboxFolderPermission, please refer to article below.

Add-MailboxFolderPermission
http://technet.microsoft.com/en-us/library/dd298062.aspx

Meanwhile, if you want to configure share permissions for file/folders in document library in Sharepoint Online, you can refer to article below.

Permission levels and permissions
http://office.microsoft.com/en-us/windows-sharepoint-services-help/permission-levels-and-permissions-HA010100149.aspx

Manage permissions for a list, library, folder, document, or list item
http://office.microsoft.com/en-us/sharepoint-server-help/manage-permissions-for-a-list-library-folder-document-or-list-item-HA010021564.aspx

Thank you.

Jack Sun