You don’t need to install anything in order to use Office 365.
To help you easily connect your desktop version of the latest version of Office, Office 2010, or Office 2007 to Office 365, Microsoft provides Office 365 customers an installable piece of software—called “Office Desktop Setup”—at no charge.
Office Desktop Setup provides many benefits, including:
Automatically detecting necessary updates.
Installing updates and components upon approval or silently from a command line.
Automatically configuring Outlook and Microsoft Lync for use with Microsoft Office 365.
Uninstalling itself from the client computer after running.
You can find and install Office Desktop Setup in your Office 365 administration center.
If your plan includes a subscription to Office, you will also be able to install that directly from the Office 365 administration center.