The two most common errors in a beginner's double haul is not reposition the hauling hand after the haul, and the timing of the haul, which we will talk about later.
So the two major things that a beginner has to learn is: (1) the haul and return of line and (2) the timing of the haul during the casting stroke.
One good way to learn the haul portion is the "Down - Up" method that Mel Krieger uses plus pantomime. You practice without a fly rod so you can do it while watching TV.
It is not the "Down" haul that is difficult for beginners. It is the "Up" return of line so they can get ready for the second "Down - Up" haul, and so on. When beginners try to teach themselves, they get the DOWN part but not the UP part. So as Mel says, the haul is a new word = “DownUp”
Initially, when you pantomime, you can time the haul to occur at the exact time that you move the rod at the START of the cast. So for the first backcast, as you take the rod back, you "DownUp" haul. When you then start the forward cast, you "DownUp" haul again. It makes doing the haul much easier if you time it with the start of the casting stroke.
However, that is often NOT the most effective time to haul. Have you ever noticed that very few of the experts’ articles tell you exactly WHEN you should haul? Why is that?
The reason is that the timing of the haul depends on how you cast and the equipment you are using. For example, if you make a backcast so that there is some slack in your fly line as you begin you forward cast, an earlier haul that removes that slack and straightens the fly line for the forward cast might improve the forward cast more than a later haul. Why? Because with an earlier haul and a straight fly line, you don't waste stroke length removing that slack.
But if you begin your forward cast with a perfectly straight line and no waves or slack, a late haul is best because it maximizes fly line velocity right before the rod stop.
Read Al Kyte's FFF article on the double haul and how the fly line and fly rod used influences when the haul is performed and how fast a haul is made.
As you become a better caster, you will find you do not need to remove slack and with the WF floating fly line that most of us use, a later haul is more optimum.
So use the pantomime to get the initial timing down, even if the timing is not perfect, a double haul is better than no haul.
In the video, Mel pantomimes long hauls. When you actually cast, I suggest practicing with short hauls at first to get the timing down. Don't move the hauling hand over longer distances which then take longer to reposition for the next haul. Longer hauls can mess up your timing. You can gradually increase the hauls when you are doing the shorter hauls correctly.
Another thread mentioned that the caster rarely double hauled and used a single haul more often. I actually double haul often even if I don't have to because it reinforces the timing and I think when I need it, I will make a better cast.