To connect to a List/Document Library with Data Synchronisation Studio on SharePoint Online you need to get the URL to your site. For example in the screenshot below our Team Site URL would be http://crmonline4u.sharepoint.com/TeamSite
You then enter this URL into the SharePointUrl Property of the 'Microsoft Office 365 SharePoint Online' Data Provider in Data Sync.
You then need to enter the credentials for your SharePoint Online environment. Note that we do not currently support environments where you have federated authentication enabled to your own AD, standard 365 Authentication is fine.
Next select the List that you wish to connect to from the ListName drop down.
And click OK to connect and there you have it!
If you get an error message when you try to connect that the system cannot load the Microsoft.IdentityModel assembly then you need to install the Windows Identity Framework (WIF) then re-start Data Sync for the changes to take affect.