There are two ways to do this. You can make use of the free "Shared Mailbox" which suits most business, with 5GB storage, no online Archiving/Retention or Legal Hold and access from Outlook and OWA only.
That last point is often a sticking point for many teams. We have become so accustomed to being able to connect to our own mailboxes from smart devices that the same expectation has formed for any mailbox we use, particularly team mailboxes. Under the bonnet, Exchange Online's free shared mailbox has a disabled user account. The username and password are not available. You can only connect using 'Outlook' or 'Outlook Web Access'.
The second and better way is to implement a common mailbox using an Exchange Plan 1 (NZ$5.10 p/m) or 2 (NZ$10.20 p/m) and set permissions to share the mailbox. Exchange Plan mailboxes have 25GB storage. Automatic online Archiving and Retention is available, with unlimited archive storage for Exchange Plan 2.
But I think the most compelling reason for using an Exchange Plan mailbox for your team's shared mail, contacts and calendar is:
You can connect to it from your smartphones and tablets.
It's worth paying the small monthly price to give your teams fully functioning mailbox, that they can connect to from their smartphones and tablets. Here in New Zealand, an Exchange Online Plan 1 costs $5.10 per month. With the permissions set up correctly and a few simple business rules, your team can share a mailbox, contacts calendar and tasks from any smart device.
Worth considering, right?