I started out trying to consume SOAP Web Services by hand like you describe - there are better ways.
There are libraries out there that will do all the work for you - no need to parse anything by hand.
Check out JAX-WS. Most Modern IDEs (Certainly Netbeans and Eclipse) also provide point and click support for building web service clients given a WSDL.
The biggest potential problem down this route is if there's no WSDL, or the WSDL is wrong, in which case the tooling I've linked might struggle.
The next safest thing would be to use an XML Parser like JAXP's SAX & DOM etc (they're right there in your JRE) to parse the response and then walk the data structures involved.
Finally you could go the string hacking route using splits or regexes but down that path lies a great deal of potential pain - there's more to the XML spec then nested tags.