Upon hearing an errant radio transmission leading you to Nuka-World and agreeing to help rescue the wounded Harvey's family, you're led unwittingly into a long corridor of death simply referred to as The Gauntlet. Here's how you beat The Gauntlet and get to Nuka-Town USA.
Immediately upon entering the first room after the train, several automated turrets activate and start shooting at you. Take cover behind the crumbled wall in front of you to hide from their line of sight. From there, start peeking out from being cover to identify where each of the turrets are so you can begin systematically taking them all out.
The next room is rigged with many, many trip wires, so keep looking down as you walk. You can disarm them by looking for the box-like apparatus at either end and interacting with it, netting you a Spring and Gears. Carefully make your way to the other end of the room, disarming tripwires as you go, and go up the stairs on the other side. Run across the collapsing wooden floor. To your right is a dead end with a locked safe, though be aware of the Tesla trap on the ceiling above it. Disarm the tension trigger on the side of the safe before attempting to open it, then pick the lock and claim the rewards.
Continue down the other branch, again disarming tripwires as you go. You'll eventually come to a tripwire anchored on the other side of a doorway, preventing you from reaching the trigger box. Shoot the tanks on the other side from a distance and wait for the fire from the resulting explosion to go out to continue on. When you're given a choice between three doors, go through the one on the left. At the bottom of a wrecked walkway, you'll come to a room full of radioactive drums, so be sure to be prepared with some radiation protection of some sort. To the far right is a locked door, which you can either pick the lock of or find a Rusty Key in the small alcove to the left of the door. Head down another collapsed walkway and into the Nuka-World Access Tunnels.
Continue following the passage until you come to a room full of turrets, which will all activate shortly after entering. When they do, quickly rush back the way you came and find the terminal in the entrance room. Hack it and choose Deactivate to shut down the turrets. Go back into the turret room and look behind the monkey toy to find the Nuka-World Storage Room Key. Go through the door and keep following the path, dispatching the Rad-Rat Pups, Tesla traps, and rigged Animatronic Alien along the way. Keep going until you come to a narrow corridor with a turret at the end. Destroy it from a distance and unlock the door behind it to score some grenades. Continue along the path and look for mines to disarm along the way.
You'll soon come to a walkway that collapses underneath you into a shallow pool full of Mirelurks to deal with. Emerge from the cave and go through the next door, disarming the tension trigger before you do. You'll come to a hallway full of grenade bouquets, which you can meticulously disarm, but it's far easier to throw a grenade of your own and explode them. Enter the next room and rush to the other end. In the broken door in the room to the left is a key. Take it and a password you find on a corpse on the ground into the locked room and unlock the door out before you choke on toxic gas.
Dispatch the ants in the next room and run through the corridor to the end until you make it to a locker room. Search all the lockers to find the Thirst Zapper water gun, which you can use to beat the Overboss and complete The Gauntlet.