In our experience, these are the four necessary ingredients in training a LGD:

Exposure

A Mentor

When you first get your Great Pyrenees, put him/her with the animals you intend for him to guard immediately. A method we use for some adults and puppies is put them in a chain link pen with a dog house in the middle of your pasture so that your new guardian can see and hear the interaction of the animals towards him and with one another.  The bond that your Pyr will form is very strong, so please try to keep at least of few of the original animals you first exposed puppy to with puppy throughout at least his first year.

When obedience, leash, or any kind of training needs to be done with pup, do it in that pasture.

Dogs, like people, learn best by the example behavior shown to them. If you can put a mature, trustworthy Pyr in with your new Pyr, you will save yourself time and work by having new Pyr watching the more experienced Pyr. Although I've put two females in the same pasture for a time, it is better to pair a boy with a girl,  and then remove the girl when she is beginning to go into heat into a separate, secure pen. I've found that the changes in her body during heat are so foremost in her thinking that she will not miss her guarding duties during the time she is safely in seclusion. When she returns to her pasture with her livestock and the male dog, she is peaceful and secure again.

HOWEVER, your pup has come from many generations of working dogs. For this reason, if you don't put your pup in with a mentor, your pup's instincts should nevertheless "click in" quite sucessfully in time.

Routine

Your working Pyr will flourish if you are consistent in your every day routine. Dogs have an internal time clock for certain activities in their lives. Their trust will grow for you if you can maintain a schedule for them and the animals around them.

Affection

Dogs have the ability to be "man's best friend" if we invest our time in a kind and gentle relationship with them. Although many folk's Pyrs are work dogs, we as owners need to be looked upon by our dogs as a pleasant break from their work day. We need to be able to easily handle them to regularly check their ears, comb their fur and check for anything unusual, and make sure their nails, especially those on the dew claws, are not too long.

"Training" methods we've used for a good LGD