Windows 7 or 8 user? Visual Studio 2012 Express for Windows Desktop is what you need.
Vista/XP user? Visual C++ 2010 Express is your download. Please be aware that on XP (and possibly Vista also) the VS2010 install might well cause problems with .NET 3.5 which makes various programs show errors they didn't before. If after installing VS2010 you find GameMaker suddenly won't open up because the updater is crashing and you're shown a Just In Time debugger window instead, please go to your Add/Remove Programs and repair your .NET 3.5 Framework. This should fix your Windows setup. It has been reported that VS2012 now supports XP due to new updates. Therefore, using VS2012 may now work, although it is recommended that VS 2010 is still used, for stability reasons.
Once you've downloaded the installer you require, go ahead and install it using the default options.
Inside GameMaker: Studio
The new File -> Preferences -> Windows needs to be setup correctly before the compiler will work properly. The defaults which ship with GameMaker are correct for Visual Studio 2012 on Windows 7/8, but these will need to be changed for other configurations. You can see the two fields for your Visual Studio and Windows SDK install locations default as in the image below:
For XP/Vista you will need to change both fields to something more like:
Obviously, if you customised the locations for your Visual Studio install you will need to change the paths here to match.