At the login screen, how do I login to a domain account?
For example, on Windows the username might be something like firstname.lastname@example.org, where the domain is contoso.local.
Edit: The AD username happens to be the same as a local username.
You need to set up Network Account Server settings in Preferences > Users & Groups > Login Options.
In the company I work for I can either use DOMAIN\username or username@DOMAIN when logging in to the AD on from a Windows Machine, but on the Mac this is not required. I just type in username and my AD password, and it logs me in.