REST is an architecture invented by Roy Fielding and described in his dissertation Architectural Styles and the Design of Network-based Software Architectures. Roy is also the main author of HTTP - the protocol that defines document transfer over the World Wide Web. HTTP is a RESTful protocol. When developers talk about "using REST Web services" it is probably more accurate to say "using HTTP."
SOAP is a XML-based protocol that tunnels inside an HTTP request/response, so even if you use SOAP, you are using REST too. There is some debate over whether SOAP adds any significant functionality to basic HTTP.
Before authoring a Web service, I would recommend studying HTTP. Odds are your requirements can be implemented with functionality already defined in the spec, so other protocols won't be needed.