Follow these instructions to begin adding a new user to a shared inbox. 

Please note that you will need to submit a helpdesk ticket for full access to the inbox. See below for details.

In Outlook, click File > Account Settings > Account Settings... :

In this window, double-click your account, or you can click Change...

Click More Settings:

Click the Advanced tab, then click Add...:

Type the name of the desired inbox and click OK:

In the settings window after you've added the new inbox, check to make sure that Download shared folders is checked, then click Apply and OK:

After you have finished this process, the inbox will appear in Outlook, but without any contents. At this point, you will need to submit a new helpdesk ticket requesting access to the inbox. Make sure to include the name of the shared inbox, as well as the name of the user requesting access (if it is for someone else).