Please don’t take this wrong way, but do you have any experience with Ajax at all? It is, if I may recall, shorthand for “Asynchronous JavaScript and XML”, and a development technique used for creating interactive web applications. The intent is to make web pages feel more responsive by exchanging small amounts of data with the server behind the scenes, so that the entire web page does not have to be reloaded each time the user requests a change.
So, whenever something changes, you need to pull that data from the server, and you will need a URL to access that content. With the Rating module you can use the template parameter to tell the module what template to use to format messages returned. The actual ajax code and implementation is left to you, and, I am afraid, somewhat beyond the scope of support we can offer on these forums.