The first time you log in to Unity, you must enter the Unity email address and password given to you by your administrator.
Click "Next" to continue.
You are now logged in.
When prompted after your initial successful login, your email address will be provided for you. Simply enter your password and click "Next".
The login window will disappear and there are no other screens at this point. You are now logged in.
Once you have established who you are, the system is locked to your user account. Your email address is provided for you as a convenience, and also because the email address associated with this system cannot be changed without reinstalling Unity.
There are two possibilities:
Look for the "Run Unity Authentication Wizard" button in the toolbar. If the button is there, click it to display the Unity Authentication Wizard. If the button is not there, then you are already logged in.
You will notice, after your first successful Unity authentication, that the interface always displays the email address you initially logged in with. Each time you reboot, this will be displayed, even though you may not have entered your Unity password.
This is because the system already knows who you are, and can perform some basic operations based on that knowledge. Your password is required to access your collaboration data, and to perform any administrative tasks.