How do I transfer an SSL certificate to a new server

GoDaddy SSL Certificates Help document entitled "Rekey certificate" may help you: https://www.godaddy.com/help/rekey-certificate-4976. Note that following this document will result in old cert being revoked and new cert being issued.

I'm not sure if GoDaddy is hosting Windows Virtual Private Server (IIS Web Server). If your server is Windows/IIS, you can export the PKCS12 cert with private key (password protected) and then import into another Windows IIS Server using instructions like those posted at digicert: How to Import and Export SSL Certificates in IIS 7 - see the "Exporting/Backing Up to a .pfx File" section. Document summary:

• Open Certificates MMC Snap-In for Local Computer Certificate Store
• Export the Cert WITH PRIVATE KEY to password-protected *.pfx file (PKCS12 format)
• Import the *.pfx file into another Windows system using same Certificates MMC Snap-In (password required to import *.pfx file).
• Choose imported cert in IIS to assign to specific web site(s).

If you're using other Web Server software or other OS, there will be a different process for copying the cert with private key for use on another system.