Many users prefer to just use Outlook on the Web. The easiest way to open a Shared Mailbox while using Outlook on the Web is to just open it:
Click on your Initials/Profile Pictures on the upper right corner and click on Open another mailbox
In the Open another mailbox dialog start typing the name of the Shared Mailbox or the Email address and it should find it. Click on the Mailbox you want and then click Open. If it doesn't find it, click on the Search Directory button.
If you have access to the Mailbox it should open right up.
HINT: If this is a Shared Mailbox you access frequently you can also create a bookmark/favorite in your Browser for it and as long as you are already logged in, it should open right up.
If it will not open for you will receive a warning message that you don't have permissions. In that case, best talk to your supervisor/or whoever asked you to open it who the owner of the Shared Mailbox is. We try to always have the mailbox owner be the one that provides access to it using a security group they can edit themselves.