You don't move it. You install it on the new computer (just as you did on
the old one) and transfer any document files. You may also want to see this
article, which will provide assistance in migrating your settings to a new
computer:
http://word.mvps.org/FAQs/General/FilesToBackup.htm.
Note that all of this is relevant only if your copy of Word/Office 2003 is a
retail one. If it came installed on your computer, then it is an OEM version
and is not licensed for any other machine.