Using stacks to implement a Queue.

MyQueue.cs

using System;
using System.Collections.Generic;
using System.Diagnostics;

namespace ConsoleApplication7
{
    class Program
    {
        static void Main(string[] args)
        {
            var q = new MyQ<int>();
            q.Enqueue(1);
            q.Enqueue(2);
            q.Enqueue(3);

            Debug.Assert(q.Count == 3);
            Debug.Assert(q.Dequeue() == 1);
            Debug.Assert(q.Dequeue() == 2);
            Debug.Assert(q.Dequeue() == 3);
            
            bool success = false;
            try
            {
                q.Dequeue();
                success = true;
            }
            catch (QueueEmpty)
            {
            }
            finally
            {
                Debug.Assert(success == false);
            }
        }
    }

    class QueueEmpty : Exception { }

    class MyQ<T>
    {
        public Stack<T>[] s;

        public int Count
        {
            get { return s[0].Count + s[1].Count; }
        }

        public MyQ()
        {
            s = new Stack<T>[2]{
                new Stack<T>(),
                new Stack<T>()};
        }

        public void Enqueue(T obj)
        {
            s[0].Push(obj);
        }

        public T Dequeue()
        {
            if (s[1].Count==0)
            {
                this.MoveItems();
            }
            if (s[1].Count==0)
            {
                throw new QueueEmpty();
            }
            else
            {
                return s[1].Pop();
            }
        }

        private void MoveItems()
        {
            while (s[0].Count != 0)
            {
                s[1].Push(s[0].Pop());
            }
        }
    }
}