We have configured AD FS 2.0 for our SharePoint 2013 site and we are using claim windows account name for login. Its working fine, but now client has changed the requirements. The new requirement is not to ask for credentials when domain (windows) user log in. For ADFS one time credential is required until the session expires. The new requirement is there should be difference between windows and external user and only to external user ADFS will be applied not to windows. I looked into it but still now do not find any relevant solution.
If your users are on your domain (using domain enrolled PCs on the same network as the ADFS servers), then you can add the ADFS server URL to the "Local Intranet" zone in their browsers and that will allow for automatic windows authentication to ADFS.
For on-premise SharePoint, that should be all you need.
With Office 365, since you tagged shaerpoint-online, there is a little more to it, there is also the Office 365 login page. With the ADFS set up as above, all your users need to do is enter username@domain or even anything@domain, to tell Office 365 to redirect them to ADFS for authentication.
You can also potentially bypass the Office 365 login page by using smart links (http://blogs.msdn.com/b/jvasil/archive/2014/05/08/o365-limiting-authentication-prompts.aspx) but I believe these are not officially supported.