How To Dock A Dogs Tail?

This is not something that you should be doing even if you have medical training.  This is a surgical procedure that needs to be done by a veterinarian.  Tail docking needs to be done within the first 2-5 days after birth or it becomes a tail amputation.  In many states docking tails at home may be considered animal abuse.  The chance for complications rises dramatically when these types of procedures are not performed by veterinarians.  Appropriate local anesthesia and pain medications can be prescribed and use by your veterinarian. 
Please do not do anything at home that will cause pain for your pets.  Do NOT dock tails with rubber bands or any kind of constrictive material.  Do NOT use kitchen scissors or any other blunt, unsanitized device.
Although you will spend more money at a veterinary clinic the surgery will be done right, be legal, and will be the least painful for these pups.  Also if you do this incorrectly you will spend more money treating these pups than it would cost to have it done by a veterinarian correctly the first time--not to mention preventing these puppies from suffering.

If you have a new puppy and it's tail isn't
already docked, leave it be.  Tail-docking
usually takes place within 10 to 14 days
of birth.  It was done originally as a method
to prevent rabies, strengthen the back and
increase the dog's speed as well as to prevent
added injuries during fighting, baiting and ratting.
Now it's done for different reasons.  Some hunting
and working dogs have their tails docked in order
to minimize burr and fox-tail tangles.  Docking is used
to keep the long hair of the tail from collecting feces.
It also is to keep dogs, like those who herd sheep
and cattle, from getting their tail caught in closing gates.
The docking of a dog's tail may be done for health
reasons, a tail injury that can't be properly repaired
and is removed .  Then there's the purely cosmetical
reason...to match breed registry standards.
If you don't have any of the above reasons, don't do it.
And if you insist on it, don't mess with it, yourself.
This is not just a chop-it-and-bandage-it job.  For one
thing, imagine how you'd feel if someone (not a doctor)
docked your finger and did it without anything for
pain, during or after?

As a vet tech, we would do dew claws and tail docks between 3 and 5 days of age. The veterinarian simply cuts in between vertebrae according to breed specification length and places one suture. Silver nitrate sticks are used to stop any bleeding.  If the the pups were too old, anesthesia was required.

A breeder takes the pups to the vet between 2 and 5 days old and has the tails docked and the dewclaws removed per breed. A few vets will dock up to 10 days old but after that is an amputation and a complicated surgery that is rarely done for cosmetic reasons because the tail is now actual bone and the nerves are more developed. A bad tail dock (why it's done at the vet) or dew removal can kill a pup or cause them problems for life and different breeds are also done different ways (different lengths of dock). If you have pups you can check you breed parent club for tail dock and dewclaw information if you intend to show or just want the pups as much in standard as possible. If your pups are not going to be shown in conformation I would probably suggest having the dews removed (less risk of tearing, catching, ect) if they are still young enough.

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This is a sergical operation performed by your vet

You need to see a vet for this, you want to make sure that this is not going to be messed up. Hope this helps, good luck to you.