Hi mathijs84,
How you go about this depends on how you want to track your goal in Google Analytics. The way that I’m familiar with is to fire off an event with JavaScript. The previous link should give you a guide on how to do that.
In terms of the plugin itself, here is an example of firing off a little bit of JavaScript when a booking is successfully submitted. The JavaScript in that snippet needs to be replaced with your Google Analytics event request.
Also, if you haven’t seen it yet, you may be interested in the developer documentation for Restaurant Reservations. It includes a big list of code snippets like this that can help you do more with the plugin.