Once you performed tasks listed in Publishing a Service. Your Basis team may have some work first time like starting some services (SICF and similar transactions) also network security.
You will provide the WSDL (Internet link) to partner, so they can consume your Web service.
You can (should) test your Web service with a tool like SoapUI, just try to consume it yourself from your desktop, if it performs well, then only network/security problems should arise.
Regards,
Raymond