Here is an SO question quite similar to this. However, through my own research, I haven't been able to find anything specific to .NET, but rather to just C#.
You can install the runtime using APT on a Debian distro by executing:
sudo apt-get install mono-runtime
You can also (assuming you have some sort of GUI such as LXDE) install a slow Mono IDE by executing:
sudo apt-get install monodevelop
