When you are in the "Media" section and have chosen a specific media to work with, a number of options will show. One of them is "Access". The "Access" area is where you can manage which of the other users that are allowed to see and publish to this media on the tab "Publishing". As seen in the picture below you can allow different departments, users, user types or groups simply by clicking one of the buttons and add the users that you want.
The ones you have allowed access to will appear below the four option buttons on the interface, where is says "Accessible for".