You need to add the MonoGame extension to Visual Studio.
Go to Extensions..., Manage Repositories..., check Visual Studio Extension Repository (Alpha channel), you should then see the extension in the Alpha channel, called MonoDevelop.MonoGame.Templates (which is still in development).
You can now go to New solution... → Other → Miscellaneous → MonoGame Solution/Project.
For a quick start, you can just check DesktopGL and no code sharing.