I've experimented with this a bit myself, and it was pretty straightforward.
Simply create a class that inherits from Page:
BasePageClass : Page
sender, EventArgs e)
// do stuff!
Then in Sitefinity, open the Title and Properties for the page you want to set the base and at the bottom input that base page class (be sure to include the full namespace).
See the attached screenshot for how I did it.
Currently you need to set it per page, but I believe a global base page is in the works for a future release. I'll send your feedback to the documentation team so that we can include this in the developer manual.
Hope this was helpful!