The web version of outlook is available at https://outlook.office.com/mail/ 

To add a shared mailbox, right click the Folders area/word (not Inbox) and choose "Add Shared folder or Mailbox"

In the box that pops up put in the email address of the mailbox and click Add.

You can also open the mailbox separately (in its own window) by going to https://outlook.office.com/mail/ and appending the email address to the url after mail/

The right-click method can also be used for the new version of outlook, but you will right click your first.last email address in the left hand pane, and it will appear under a folder titled Shared with me.