How to add second Internet domain?

Hello all:

I'm running MS Exchange 2003 (Exchange Server for Small Business) on a single server. My client has just registered a new Internet domain name and wants certain employees to use this new domain (along with the old one) for their email address. How do I configure Exchange to process multiple domain names??? I tried adding a new SMTP Connect with the new domain name and setting this new email domain in Active Directory for my user account, but it doesn't seem to work. I hope I'm just missing something simple! :) I haven't been able to find very much documentation on this either... TIA.

Thanks,
Jon