Do a search for Mountain Man Jim's posts on training, he has some excellent advice.
Socializing the dog is important. Unless you live WAY WAY WAY out in the boonies, and no one, but no one, including the mailman or the vet or a neighbor's kid selling Girl Scout Cookies, is ever going to set foot on your property, you MUST socialize a Pyr.
My neighbor did not socialize her Pyrenees, because she believed that you do not socialize a guard dog. Two hard-bitten and irate joggers later, the town told her she could fence her property or have the dog euthanized.
In contrast: My Pyrenees has been very carefully socialized, and he knows the difference between Bad Person/Dog and Good Person/Dog. When my neighbors walk their sweet-as-pie poodle mix past the house, he jumps around like a goof and tries to play (with a 20 lb. dog...yeah, it's interesting); yet when the neighbor with the big biting bugger of a Pyr walked her dog past the house, Charlie chased it across the street and held it at bay.
The thing is, an angry Pyr is 150 lbs. of teeth and claws and extra claws. They are not just big, they are athletic and they can outrun a human. They are determined and don't heed humans 100% of the time, alpha or not. If a Chihuahua is unsocialized and bites people, well, maybe you'll need a few stitches. If a Pyr is unsocialized and bites, they will kill someone.
Despite extensive socialization, Charlie has chased off the Evil Neighbor Dogs, foxes, coyotes, deer, rabbits, fishers, opossums, red-tailed hawks and raccoons. He's a very good guardian--out of the five or so chicken keepers in our neighborhood, I have lost about 4 chickens out of 26 to predators. In contrast, my neighbors have lost 30+ each--they regularly lose their whole flock. I'm the only one who has an LGD. Coincidence? I think not.