This is done by creating a Shell Extension, specifically by creating a Folder View. The topic is too broad to go in depth here on how to create one from start to finish but perhaps knowing the correct term and having those links will at least help get you started.
Note that if you want to use .NET to write your shell extension Microsoft only officially supports using .NET 4.0 or newer for writing shell extensions. This is because 4.0 is the version that supported In-process Side by Side.