XNA 4.0 came out in late summer 2010, and XNA Game Studio 4 was available as an add-on to both Visual Studio 2010 and Visual C# Express 2010. More recently, Visual Studio 2012 and Visual Studio Express 2012 for Windows Desktop were released, but XNA Game Studio 4 could not be added on to either of these. Instead, if you want to make XNA games, you're stuck working with the now out-of-date 2010 editions.
For what it's worth, a similar thing happened when the 2010 versions of Visual Studio came out. XNA developers were stuck using VS 2008 for a little while until they could get a new release put together.
But I know there are people out there who are really wanting to do XNA development in the new
An Incomplete Picture
What I've shown you so far, is a very incomplete picture. As I have more time to do more with this, I intend on adding in some additional information here, but please feel free to add questions and other tips for getting XNA to work in Visual Studio 2012 on the troubleshooting page.
To the people over at Microsoft: if you want any help getting XNA 4.0 to work in Visual Studio 2012, I'd be happy to donate my time to help. You know where to find me.