You use a proxy!! ArcGIS Server provides you one here. More information oh how a proxy works can be found on the Yahoo Developer Network.
I named this post Cross domain XMLHttpRequest because in the context of ExtJS, the ScriptTagProxy doesn't support HTTP POST calls. Therefore, you would use HttpProxy (with a POST method) to access the proxy on the local server. Remember to pass the parameters as properties (instead of concatenating them to the URL).