Current information on development in Linux environment: (information from Karl Smelitzer, as of 10/2009 )
Mono: an open-source implemention
of the .net framework:
http://mono-project.com/Main_Page
Monodevelop: an open-source IDE
designed for building Mono applications
http://monodevelop.com/
Mono.XNA: an unfinished, but growing open-source
implementation of the XNA framework using OpenGL
http://www.monoxna.org/
TAO Framework: C# bindings that might help
http://www.taoframework.com
To build simple C#/WinForms application you'll only need Mono. Installing Monodevelop will probably also make your life much easier for checking references, etc. If you are using Ubuntu (the most popular Linux distribution at the moment) you can install both by issuing the following command from a terminal:
sudo apt-get install mono-utils
mono-xsp monodoc-http monodevelop