Can anyone explain to me how to subclass a webpage that someone else wrote with their codebehinds in C#?

One company we are working with wrote a few web pages that call their API. I want to add a smidgen of new functionality to it, while maintaining the same look and feel. I was told that I could subclass their page, but I have no clue on where to start on this. I would like to write my page using VB.net code behind, but I can do C# if necessary.