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