How do you test private methods with NUnit?

Generally, unit testing addresses a class's public interface, on the theory that the implementation is immaterial, so long as the results are correct from the client's point of view.

So, NUnit does not provide any mechanism for testing non-public members.

While I agree that the focus of unit testing should be the public interface, you get a far more granular impression of your code if you test private methods as well. The MS testing framework allows for this through the use of PrivateObject and PrivateType, NUnit does not. What I do instead is:

private MethodInfo GetMethod(string methodName)
{
    if (string.IsNullOrWhiteSpace(methodName))
        Assert.Fail("methodName cannot be null or whitespace");

    var method = this.objectUnderTest.GetType()
        .GetMethod(methodName, BindingFlags.NonPublic | BindingFlags.Instance);

    if (method == null)
        Assert.Fail(string.Format("{0} method not found", methodName));

    return method;
}

This way means you don't have to compromise encapsulation in favour of testability. Bear in mind you'll need to modify your BindingFlags if you want to test private static methods. The above example is just for instance methods.