Contacts can be saved in the Outlook PST file and/or in the Windows Address Book.
In first case you just need to copy the PST file to the new computer and open it in Outlook. If it is opened as second PST file, you have also to enable the contacts of this second PST.
In second case you may find the WAB file containing the address book and copy it to the new computer, then connect it to the Windows Address Book.