For the apps I\'m writing in Visual C#?
I would suggest setting up a VM with just your software installed and then just alter the ram and processor specs on it and retest.
It will take a little while but this would be a great way to do determine it and see what areas that you application could be enhanced.
Testing.
(No, really, that's all there is to it.)
Well, the minimum requirements for your application written in C# is probably going to be the .Net framework, which has a nice page here listing the requirements for the various versions.
How usable will your app be using the recommended minimum? You'll have to find some hardware (or use a virtual machine see comments) and try it out.
It depends from the kind of application you are writing. For example a 3d videogame could require DirectX capable hardware. If you are writing an office app (wordprocessors and so on) every modern computer with .NET framework is enough :)