Testing can only prove that there is a bug. No testing can prove there is no bugs, ever.
NUnit is effective here, but the results of the tool can be only as good as testing code, no better; and the testing plan, test cases and testing code is something which you do, not the tool. The tool is only the way to organize it all and automate running of the tests. No more, no less.
How to implement it? Strange question. By learning the tool using documentation and the tool itself:
http://en.wikipedia.org/wiki/NUnit[
^],
http://www.nunit.org/[
^].
The documentation is comprehensive:
http://www.nunit.org/index.php?p=docHome&r=2.5.10[
^].
You don't expect me to double the documentation, do you? :-)
Perhaps, start with "Getting started". :-)
Maybe, just one idea: all the testing artifacts, testing documentation, all the testing code should be the integral part of the project itself. Project is the sum of its deployed part and everything else, and deployed part is the smaller part. Everything else is needed to "support programming as human activity". Your project can be as successful as its maintenance, no better. The testing is the integral part of it. All the artifacts should be integrated in you code base under you Revision Control System. This is quite a different story though…
Good luck,
—SA