If you want to launch the WinForms app from a web page, the best approach is probably to use ClickOnce technology. It allows you to publish your application directly through a web page (no separate installer needed).
ClickOnce is a deployment technology that enables you to create self-updating Windows-based applications that can be installed and run with minimal user interaction. Visual Studio provides full support for publishing and updating applications deployed with ClickOnce technology if you have developed your projects with Visual Basic and Visual C#.
http://msdn.microsoft.com/en-us/library/t71a733d(v=vs.110).aspx
ClickOnce also works with C++ apps, but there are some additional steps
http://msdn.microsoft.com/en-us/library/ms235287.aspx
There's an excellent answer on Stack Overflow that reviews some things to be aware of. Suggest you read through that as well
https://stackoverflow.com/a/2365481/141172
If you want to launch your application (possibly including parameters) from a web page, one approach is to have the application register a protocol handler. A protocol handler allows an application to react to a URL with a new protocol that you define, e.g. myappname://TheFileToOpen
http://msdn.microsoft.com/en-us/library/aa767914(v=vs.85).aspx