A javascript http request doesn't differ at all from any other http request in how it's performed. Some data is sent to some web server indicating a specific resource as its target. The web server passes on the data to whatever is found there, collects the output and sends it back to whomever made the request.
This is how the page is displayed to begin with. The __doPostBack function then deals with new http requests to inform the server that it wants information that belong to a specific link. The response however, may come in any variety of formats (other than (X)HTML), since the web browser is no longer directly responsible for parsing the data. This is done through javascript. And although the response may be sent as (X)HTML, it's common to send it as JSON (javascript string object notation) so that you can get javascript data structures (arrays and object) from the response, XML or plain text.
You only have to figure out what is sent in these requests, and then mimic the same requests. After that you can inspect the responses and deal with parsing them as necessary.
