There are two ways. If you want to only give permissions for the Calendar, use the first part.  To set permissions on more than on folder at once (say, the “Inbox” and “Calendar”), it’s better to use the second approach.  The second approach is more intuitive/obvious from a user standpoint.

In either case, do it on their computer that has the calendar to be shared as they are logged on.  Afterwards, the person who needs access to the calendar would then use his/her Outlook and do a File, Open, Other User’s Folder to locate the shared calendar.

(1st way) Set sharing permissions for a folder

1. If the Folder List is not visible, click the View menu, click Folder List, and then select the folder you want to share with another person.
2. Right-click the folder you want to share, and then click Properties on the shortcut menu.
3. Click the Permissions tab.
4. Click Add.
5. In the Type name or select from list box, type or select the name of the person you want to grant sharing permissions to.
6. Click Add, and then click OK.
7. In the Name box, click the name of the person you just added.
8. In the Roles box, click the permissions you want.

(2nd way) Set sharing permissions for more than one/all Outlook folders

1. To set permissions for all of your Outlook folders simultaneously, use the options on the Delegates tab (on the Tools menu, click Options).
2. Click the "Add..." button
3. Select the person with whom you wish to share your Outlook information.
4. Click the "Add->" button to select him/her.  (Or double-click the name.)
5. Click "OK"
6. Use the drop-down menus to set permissions for one or more of your folders.
7. Click "OK"
8. Click "OK" again and you're all set!