If you don't need to modify any source, I would recommend you instead get a nightly build and use that instead.
Installing an mpack in Xamarin Studio
This should be the easiest method to get MonoGame working in Xamarin Studio. Go to the downloads page and click on "MonoGame for MonoDevelop".
This will download a .mpack that you can install directly by going to the "AddIn's Manager" in Xamarin Studio. Choose "Install from file" and locate the .mpack and you should be good to go
Using .dlls from a nightly build
Go to the downloads page and then click on "MonoGame for Visual Studio" under Development Builds. That will get you the latest build from the MonoGame TeamCity page.
You can then unzip the executable and grab the .dll files which will be in the folder "Assemblies" and use them as references in your Xamarin Studio project.
if you really want to compile it, it's not too bad either.
Compiling From Source
Either fork the MonoGame Develop repository or download the project as a .zip from GitHub and run ProtoBuild.exe
That will create all of the .csproj files for each platform, which you can open in Xamarin Studio to use as library projects.