1.   Please open Outlook 2007.

2.   Right click on Inbox and select Properties.

3.   Click on Permission.

4.   Click on Add.

5.   Type the name on search for the user with whom you wish to share the mailbox or folder.  Click Go

6.    Select the User from the list and click on Add

7.   Under permission select appropriate permission level.  The permissions are listed in the drop down.

8.    Click apply and OK.

Related Links:

Exchange Server 2007

Hosted Outlook

Outlook Web App