Just don’t. It does not work as proclaimed and has a big chance of traumatizing your dogs and influencing their behavior for their whole life. Alpha Dog is using your position as a relevant member of the group to inflict unnecessary violence in situations where dogs actually learn from example or operant conditioning.
As a little analogy, Alpha Dog is like building a house just using screws and a hammer. In certain situations and with certain screws, you can and should indeed hammer in the screw. But there are a ton of other situations, in which only resorting to violent domination as part of operant conditioning is hindering your training efforts.
Like sit, stay and heel are in no way necessary to be punished to work. Actually punishment is meant to reduce the likeliness of a behavior because it would be stressful otherwise. All of those things you want your puppy to do are those you would want it to do without being stressed. Simply because stress (cortisol to be exact) lowers the ability to learn and the relaxing or focusing effect of the situation you want to use them in, like walking your puppy or training something else.
A stressed dog will relieve itself a lot less often, will not really relax while walking and will stop showing emergent behavior in other training situations. All it will learn is that being and cooperating with you is a stressful but necessary thing to survive, because you are (in the eyes of your dog – please don’t be offended) a violent moron who is unable to learn the subtleties of communication and is only able to communicate like a bully if you apply this Alpha Dog Nonsense.
I’m not saying that punishment in the sense of operant conditioning is not necessary in certain situations, but the severity of the impact of a punishment can’t be overstated. Especially if it is done by the owner of the dog. All trust and bonding can be broken with one single overdone and wrongly timed punishment. Your dog can end up traumatized and having more problems than it had before. Your access to willful cooperation might be lost, and the gates to a quickly escalating and fearful violent dog could be open now.
Punishment, and especially Alpha Dog is all about unnecessary punishment of almost everything, is something that you should not do alone. You should not do it without professional counsel and education how and when to punish. You should also have established a wanted positive behavior for the dog to turn to, instead of punching your dog because it did not sit down like you wanted it to, but not having the means of telling it HOW you actually want it done. And even in this case it is way more effective to make your dog want to do it instead of fearing the consequences.