This cannot be done with straight JavaScript unless the web service is on the same domain as your page.
If the web service is on another domain then you will have to use a proxy page on your own domain that will retrieve the results and return them to you. If you are going to do that then you should use something like the lib that timyates suggested because you do not want to have to parse the results yourself.
If the web service is on your own domain then don't use SOAP. There is no good reason to do so. If the web service is on your own domain then modify it so that it can return JSON and save yourself the trouble of dealing with all the hassles that come with SOAP.
Short answer is: Don't make SOAP requests from JavaScript. Only use a web service to request data from another domain, and if you do that then parse the results on the server-side and return them in a js friendly form.