Importing and Exporting Contacts in Microsoft Outlook

1. In Outlook, on the File menu, click Import and Export.
2. Click Export to a file, and then click Next.
3. Click Comma Separated Values (Windows), and then click Next.
4. In the folder list, click the Contacts folder, and then click Next.
5. Browse to the folder where you want to save the contacts as a .csv file.
6. Type a name for the exported file, and then click OK.
7. Click Next.
8. Click Finish.

That gives you a comma separate list of your Outlook Contacts. Transfer that to your new computer, then you can import them into your new version of Outlook with the following steps:
 

1. On the File menu, click Import and Export.
    
2. Click Import from another program or file, and then click Next.
    
3. In the list, click Comma Separated Values (Windows), and then click Next.
    
4. Click Browse, locate your file, and then click Next.
    
5. Click your Contacts folder or another folder that contains contacts, and then click Next.
    
6. In the list, click the file that contains your address list, and then click Map Custom Fields.

You could also choose Personal Folders (*.pst) instead of Comma Separated Values.
If you use personal folders you will not have to do any field mapping.

That should get you going. If you need more help here are two reference pages from Microsoft, one on Exporting Outlook Contacts and another on Importing Outlook Contacts.