You can get into Skype for Business in two ways: via the Office 365 or via the Skype for Business desktop app. Let's look at both ways in detail.
How to get into Skype for Business
Getting into Skype for Business via Office 365
When you log into Office 365, you are automatically logged into the online version of Skype for Business. People can see your presence and contact you:
It may take a minute or so before your presence updates. There may be times where you are signed out and will need to sign in. Click on your persona to log in and/or change your presence.
You can see your contacts and IM them when you go to Outlook and click on Skype for Business in the suite bar.