As with any livestock with respect to predation, it's all about location, location, location...
Fencing is going to be your number one consideration both for containment of your livestock as well as a first line of defense against predation. Your fencing is typically ~4' high (woven wire "field fence" or sheep & goat fence or horse fence) and will keep your animals in, but a coyote can jump straight up and over it. If it's a purely barbed wire fence, they'll go right through it or under it. Many folks (1st type fencing) add to this a strand or two of barbed wire above the lower fencing or a strand or two of hot wire at the top. Some folks use high tensile strength smooth wire that is electrified in place of either of the above. You can runs strands to any height you desire, alternating positive (hot) and negative (ground) wires.
Many predators will "respect the fence", especially during daylight hours, knowing that typically the inside is a dangerous area to them (humans with guns, LGDs, etc). But there are those who won't/don't, and this is what a "night pen/barn" area close to the house is all about. You provide treats to the animals when you first get them so they learn to come when called so you can "lead them" into said night area for their safety. I feed my goats their dinner of pellets and hay inside their enclosure starting right before dusk. They all know when dinner time is and are generally inside waiting (im)patiently for me to bring them their due. After feeding, I simply close the gate with them inside. One side of that pen is the fencing at the back edge of my back yard.
I have an LGD that patrols outside the perimeter of the night pen in the pasture, and a house dog that patrols inside the yard fencing around the house. Either or both alert when there's something they are uncomfortable with. I hear coyote packs howling all the time on all sides, typically at dusk, and at times through the night. I've watched singles and pairs saunter across my back pasture (behind the primary use pasture & ~250 yards away from the back porch), and watched one cross the property up in the front pasture once, crossing the driveway and continuing over into the neighbor's property through the woods. I have shot at them several times but have not killed any. Most of the time, they show up at odd times when I'm not armed and unable to get armed without scaring them off first. None have hassled any of my goats and I've lost no animals to predators.
Coyotes have become quite brave and packs will hunt dogs. Generally one coyote will tease the dog into following and lead the dog away to be taken down by the pack. Generally, they won't mess with an LGD but even LGD's have been killed by coyote packs. LGD's typically work best in a team environment. How many LGD's depends on a lot of things, notably; the concentration of predators, types of predators, size of the area they will be required to keep safe, and number of animals they'll be protecting. There's quite a bit of material available on the site regarding LGDs... I love mine. They are very special animals. I am prepared to assist/back up my dogs should the need arise. If there's a serious threat, I can tell by their reactions and proceed outside, armed, to make sure they, as well as the animals they are protecting, are also protected.
Most folks with cattle don't have to worry about predators except during calving. Bears or cougars (and possibly wolf packs) will take down a cow, but generally speaking no other (wild) predators are a concern. This isn't the case with sheep and goats. Anything bigger than a fox is a concern for adult animals and even foxes can take down babies given the opportunity. A hungry predator will do whatever it needs to do to eat. When closer to civilization, the bigger threat is dogs... strays, your neighbor's, and even your own. Most LGD owners will not allow their house dogs in the areas they expect their LGDs to protect. It sends a mixed message to the LGD as to what dogs are allowed in their area. The LGD should and wants to "own" their pasture and should not allow ANY dog or other predator inside it.
