You can download MonoGame in either as a binary installer or source code.
The Installer will get you up and running quickly, but if you want to make changes you will need to get the source code.
There are a few pre-requisites that you should be aware of for the various platforms:
|Windows||Windows 8||iOS||Android||Mac OS X||Linux|
|Machine||PC||PC||Mac||Mac or PC||Mac||PC|
|IDE||Visual Studio||Visual Studio||Mono Develop||Visual Studio or Mono Develop||Mono Develop||Mono Develop|
The Windows Installer supports for following platforms, Windows, Linux, Android. There is an Add In package for MonoDevelop which includes Windows, Linux, Android, Mac and iOS, although you will need a Mac to use the Mac and iOS project types.
If you want to get hold of the latest source code you can get that from Github.