How do I create an application domain and run my application in it?

It should probably be noted that creating AppDomains just to get around something that can be fixed with a constant string is probably the wrong way to do it. If you are trying to do the same thing as the link you noted, you could just do this:

var configFile = Assembly.GetExecutingAssembly().Location + ".config";
if (!File.Exists(configFile))
    throw new Exception("do your worst!");

Recursive Entry Point :o)

static void Main(string[] args)
{
    if (AppDomain.CurrentDomain.IsDefaultAppDomain())
    {
        Console.WriteLine(AppDomain.CurrentDomain.FriendlyName);

        var currentAssembly = Assembly.GetExecutingAssembly();
        var otherDomain = AppDomain.CreateDomain("other domain");
        var ret = otherDomain.ExecuteAssemblyByName(currentAssembly.FullName, args);

        Environment.ExitCode = ret;
        return;
    }

    Console.WriteLine(AppDomain.CurrentDomain.FriendlyName);
    Console.WriteLine("Hello");
}

Quick sample using a nonstatic secondary entry point and MarshalByRefObject…

class Program
{
    static AppDomain otherDomain;

    static void Main(string[] args)
    {
        otherDomain = AppDomain.CreateDomain("other domain");

        var otherType = typeof(OtherProgram);
        var obj = otherDomain.CreateInstanceAndUnwrap(
                                 otherType.Assembly.FullName,
                                 otherType.FullName) as OtherProgram;

        args = new[] { "hello", "world" };
        Console.WriteLine(AppDomain.CurrentDomain.FriendlyName);
        obj.Main(args);
    }
}

public class OtherProgram : MarshalByRefObject
{
    public void Main(string[] args)
    {
        Console.WriteLine(AppDomain.CurrentDomain.FriendlyName);
        foreach (var item in args)
            Console.WriteLine(item);
    }
}