If it works via AJAX, you have to figure out the format of the message passed back and forth. You could look at the raw transmission as memcpy suggests, but that may not help very much all by itself. You also need to find the javascript calls involved and see how the data in the message is serialized, where it comes from client side, and how the response is used. This will be tedious as google compacts their scripts and tend to use very uninformative and minimal variable names, etc. I haven't used the Chrome tools, but presuming they do something like Firebug, you should be able to watch the transmissions occurring and possibly trace the js calls. You then need to mimic their output (which you could do in C or python or whatever), keeping in mind that some of the information maybe, eg, a cookie value intended to prevent people from easily spoofing the service this way. It cannot be made impossible, nb., but it can be made more difficult: if a cookie is involved, you will have to figure out how it came to be, a way to get such a token first, and then use it properly in the "ajax" exchange.
Unfortunately, Angel45, your understanding of how web applications work sounds a little simplistic, meaning you may have to learn a lot just to attempt this. Again, not impossible, but if the official API looks easy enough to use, it may be worth the $20 as it will save you literally days and days or weeks of study and experimentation, etc.
http://en.wikipedia.org/wiki/Ajax_%28programming%29
http://en.wikipedia.org/wiki/JSON
