This question is related, but NOT a duplicate: How to install XNA game studio on Visual Studio 2012?
I read the above mentioned post, and have got xna projects opening, but I now have a problem.
Some of the references to the XNA framework aren't found:
Microsoft.Xna.Framework.Avatar
Microsoft.Xna.Framework.GamerServices
Microsoft.Xna.Framework.Net
Microsoft.Xna.Framework.Storage
Microsoft.Xna.Framework.Video
And all references to Microsoft.Xna.Framework.Content.Pipeline
Without these, I can't compile or run any games that I've made. I can't find the dll that contains these, or where I should put them.
The installer for XNA Game Studio 4.0 has some issues on Windows 8. The installation process fails and removes all installation files. The fact is that the main installer extracts the following installers (at c:\Program Files (x86)\Microsoft XNA\XNA Game Studio\v4.0\Setup):
The conflict is with the first one. So if you manually install all others, XNA should work fine. The problem is that after the installation failure this files are automatically deleted. My solution is to halt the installation process (using the task manager) in the moment when an error was detected, this way the installer don't have time to erase the installation files. Once you have the files you can install it without repeating the procees. It worked for me!!!
UPDATE: March 3, 2014
Use the download for VS2012 and VS2013 at this link: https://msxna.codeplex.com/releases. I have no idea of the legality on that project (the developers seem to have decompiled XNA), but it did help me ease the pain of needing VS2010 in order to utilize the content pipeline.
Old Answer
See: How to work around a possible XNA Game Studio or Windows Phone SDK install failure on Windows 8