There is is a Stack Overflow question quite similar to this, *[Mono on Raspberry Pi][1]*. However, through my own research, I haven't been able to find anything specific to .NET, but rather just C#.

You can install the runtime using [APT][2] 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 with:

    $ sudo apt-get install monodevelop

For [Arch Linux][3] ARM you need to install the runtime via [Pacman][4], like so:

    $ sudo pacman -S mono

The Mono IDE can be installed in a similar fashion:

    $ sudo pacman -S monodevelop

  [1]: http://stackoverflow.com/questions/10213600/mono-on-raspberri-pi
  [2]: http://en.wikipedia.org/wiki/Advanced_Packaging_Tool
  [3]: http://en.wikipedia.org/wiki/Arch_Linux
  [4]: http://en.wikipedia.org/wiki/Pacman_%28package_manager%29