The base functionality delivered by easyXDM is to, without any server-side dependencies, pass string based messages between two domains in a fast, reliable and secure way.
With easyXDM this is easily done using the easyXDM.Socket class, a class that encapsulates the different transports and behaviors necessary to achieve speed, reliability and security.
To receive messages you simply set the onMessage method in the configuration
var socket = new easyXDM.Socket({ ..., onMessage: function(message, origin){ alert(message); } });
.. and to send messages you simply use the instantiated sockets .postMessage method
socket.postMessage("the string I want to send to the other end");
Remember, each Socket is bi-directional, so you only need to instantiate a single one per channel.
Take a look at the example here.