The simplest way is probably to add a WebBrowser control to your application and point it at the page you want to save using the Navigate() method.
Then, when the document has loaded, call the ShowSaveAsDialog method. The user can then save the page as a single file, or a file with images in a subdirectory.
[Update]
Having now noticed "programatically" in your question, the above approach is not ideal as it requires either user involvement or delving into the Windows API to send input using SendKeys or similar.
There is nothing built-in to the .NET Framework that does this all of what you ask.
So my approach revised would be:
- Use System.NET.HttpWebRequest to get the main html document as a string or stream (easy).
- Load this into a HTMLAgilityPack document where you can now easily query the document to get lists of all image elements, stylesheet links etc.
- Then make a separate web request for each of these files and save them to a subdirectory.
- Finally update all relevent links in the main page to point to the items in the subdirectory.
In effect you would be implementing a very simple web browser. You may run into issues with pages that use Javascript to dynamically alter or request page content, but for most pages this should give acceptable results.