Authentication is a key to access corporate resources, hosted either on-premises (you can use ADFS to authenticate against Exchange to access your mailbox) or in the cloud (Office 365, Azure, Salesforce…).
While Microsoft is working hard to make authentication process to his services a little bit easier for end-users (password synch, seamless single sign-on…), you may still rely on federated authentication using AD FS (Active Directory Federation Services).
Troubleshooting authentication issue is always a complicated task.
To help and assist you in this hard task, you can go to the new Microsoft website: ADFS Help (https://adfshelp.microsoft.com/)
At this time, there is only the Tools section available; the troubleshooting piece will come later.