How can I share mailboxes attached to my Exchange account in Outlook 2003?
Instructions with screen shots can be found here:
University of Connecticut - Configure a Shared Mailbox in Outlook 2003/2007
There is few ways, depending your access level on the Exchange server.
First one, I'd just give a delegates access from Tools - Options - Delegates and from there, share calendar, inbox and other things you need to give. Also, don't forget to set proper security on your MAILBOX and your Inbox. When this is set, you can change permissions on different folders you need to share with the proper level access.
If you have access on the Exchange server, you can set a Full Mailbox Access from it to the user needing access. It's quite simple to do (You can also do it from AD if you have the Exchange plugins) but you will share everything with full acces. Read-Write-Modify so be sure the person won't srew anything and also, have a backup run daily. That's what I'd do.
It's now up to you to check which way is the best one for you! Good luck!