On the Archive Manager page, choose from the tabs the type of item you wish to archive or reinstate - you have the choice of Tasks, Risks, Projects and Departments. Apply any filters that will help drill down to the information you need and then select whether you want to see the "Active" or "Archived" items within those parameters. An item list will then appear (Tasks in the example below) allowing you to check the right hand column of those items and send them to the archive or back to the main system as needed.
If you click "Show Archived" then the "Archive" button on the right will switch to "Reinstate" and makes items active in the main system again.
NOTE: Archiving Projects will also archive all constituent Task Groups and Tasks, while archiving Departments will archive all constituent Tasks for which that Department is the sole owner.