Once a Shared Mailbox is added to Outlook, searching within it is similar to searching on a Primary Mailbox.
Open Outlook.
Select a folder within the Shared Mailbox on the Folder Panel on the left.
Type the query in the Search Box on top of the Ribbon (Tool Bar).
Execute the Search by pressing Enter or clicking on the Magnifier Button on the right of the Search Box.
The Message List will return results based on the Search from that selected folder on the Shared Mailbox.