For getting started with Skype for Business, including how to install it on Windows, read Getting Started with Skype for Business at Trinity.
In order to login to Skype for Business on many mobile and MacOS apps, you will need both your full firstname.lastname@example.org address and password, AND, under “Advanced options,” your shorter email@example.com filled in for “Signing in as.”
When you open the app for the first time, your sign in screen should look like this (more or less):
Tap or click on “Advanced options” to access the “Signing in as” setting, where you will enter your firstname.lastname@example.org (typically your first initial and last name):
Then return to the previous screen and enter your full email@example.com and password:
You should now be able to log in to Skype for Business. Commence communicating.