Shortly after leaving the vault, you can find a trusty furry companion a few meters away from your hometown of Sanctuary. Follow the road leading to Red Rocket Truck Stop where you can find the lone dog. Talk to him to befriend him and he'll be your friend forever. Dogmeat (he'll get the name later as you progress in the first main story quest) is a very useful companion.
Extra skill/ability
There are also certain apparels that can be worn by Dogmeat like dog collars, bandannas, and of course, dog armor. These equipment only provide cosmetic changes and doesn't have any damage reduction properties. To equip Dogmeat, transfer the apparel to him, switch to his inventory and press Triangle.
Dogmeat is also a very effective combatant, capable of taking considerable damage, can rip of limbs, and pin down enemies to give you a clear shot. In short, after leaving the vault, find and befriend him and he'll be with you for life. Like all companions in the game, Dogmeat will not die. He'll be gravely wounded and will whimper but you can just use a stimpack to get him to action. He'll also recover automatically over time and join up with you without too much fuss.
Dogmeat can be dismissed temporarily and you can order him to return to any of the settlements you have cleared so far. Take note that if you sent him to Sanctuary, Dogmeat will rest in one of the many doghouses in town. To make it easier for you, collect all the dog houses in Sanctuary then relocate one of them near your workshop so you can find Dogmeat easily.