In my previous blog, I had explained how to add a message in queue. Now here is the sample code to read the message from a queue  

CloudStorageAccount storageAccount = CloudStorageAccount.Parse(RoleEnvironment.GetConfigurationSettingValue("torageConnectionString"));
                     CloudQueueClient queueClient = storageAccount.CreateCloudQueueClient();

                     // Retrieve a reference to a queue
                     CloudQueue queue = queueClient.GetQueueReference("queueName");

                     if (!queue.Exists())
                         continue;//In case queue is not found

                     //Retrieve message from queue
                     CloudQueueMessage retrievedMessage = queue.GetMessage();
                     if (retrievedMessage == null)
                         continue;//If Message is found null

                     string message = retrievedMessage.AsString;//Retrieve message in as string 

                     queue.DeleteMessage(retrievedMessage);//After reading the message, we should dequeue it so that it does not come in process again

This way we can retrieve message from Azure queue