To install your Office 365 on Mac login to https://portal.office.com with your credentials, click on Install Office apps and Office 2016.
In Downloads folder there should be Microsoft Office 2016 Installer.pkg file. Double-click the installer.
NOTE! Name of the installer might vary slightly.
On the first installation screen click Continue.
Review license agreement and click Continue -> Agree -> Continue -> Install.
Provide your Mac credentials and click Install software.
After the installer finishes up the installation click Close.
Go to Launchpad and click on Office 365 application eg. Word or Excel.
Click Get started > in the window that pops up and login with your Office 365 credentials when prompted to activate the license for the product.