In most cases you can simply send an email to the address shown in the Admin Contact - however random it may look.

Usually the email is automatically forwarded to the owner of the domain, using the real email address that the whois service has on file.

It does works with GoDaddy's whois protection service.

In rare cases this method doesn't work, for instance with domains protected by ResellerClub - possibly because their whois protection is given away for free.