Start from creating shared folder you'll be able to access from both computers over your network, or get external hard / flash drive ready - one you can plug in and access on both computers if network is out of the question.
Now, open your "old" computer Registry Editor (Start / Run REGEDIT command), and navigate to \HKEY_CURRENT_USER\Software\Microsoft\Windows NT\CurrentVesrsion\Windows Messaging Subsystem\Profiles. Right-click Profiles folder and left-click Export on the menu - browse and safe exported REG file to your previously prepared shared directory or external drive.
Next, navigate to your Outlook Signatures folder - by default it's located under system drive's Documents and Settings\[your username]\Application Data\Microsoft. Right-click Signatures folder and left-click Copy... Go back to your shared folder or external drive, right-click anywhere on the empty folder space and left-click Paste - Your Signatures folder is now copied to your shared folder or external drive.
Finally, navigate to your Outlook folder located by default under computer's system drive \Documents and Settings\[your username]\Local Settings\Application Data\Microsoft. Right-click Outlook folder, left-click Copy... Now, go back to your shared folder or external drive, right-click on the empty space there and left-click Paste... Keep in mind that Outlook data folder may contain large PST and OST files and may reach well over available space on your shared folder or external drive. Please make sure you have sufficient free space available on your shared folder / external drive to accommodate all your data !
You have now collected all your Outlook data and settings and ready to migrate them to your "new" computer...
Access your shared folder or external drive on your "new" computer, double-click your saved REG file, confirm import into the registry (you will see "successful import" message when it's done).
Copy your Signatures folder, then paste it to your system drive's Documents and Settings\[your username]\Application Data\Microsoft.
Now, do the same for your Outlook personal folders / data files - Copy and Paste Outlook folder to your system drive's \Documents and Settings\[your username]\Local Settings\Application Data\Microsoft.
Open Outlook 2003 on your new computer and enter your email passwords as prompted - you should have all your email accounts, rules and alerts, data and emails there.
Above instructions are geared towards somebody who is familiar with Microsoft XP Operating System and can comfortably perform basic file and registry operations. Also, be careful when copying files and folders to directories that already contain files and folders as those can easily get overwritten, and so is your previously saved data - in this article we assume that Outlook on the "new" computer has not been configured and used previously.