First off, web services can take different forms. SOAP is a popular one, as is REST. Both use HTTP as the transport protocol. The
WebServicesFaq points to several articles that contrast these two styles.
So if I am using http ://address/webServiceName/method?var1=value to call a web service, does it mean that I am not using any SOAP to tranport my request?
If that's all you're sending, then yes - there's no SOAP. SOAP would be sent in the body of an HTTP request, and would typically not have parameters in the URL.
If yes, then how does the web service handle my request? What protocol/ format am I using? Am I using plain HTTP get to transport my request to the web service?
What you're using is closer to REST-type web services, where all parameters are transported as part of the URL (though, confusingly, not necessarily as URL parameters).