They have several methods:
1. They are very stealthy. All angles, no masts, no protrusions, no barrels, etc. Very hard for an enemy to find and lock on to.
2. They have electronic counter-measures galore to electronically jam and confuse missiles. Even butn their electronics out.
3. They have systems that blast stealthy clouds of material and/or chaff into the air to have missiles lose their lock.
4. They have anti-missiles, quad packed into each vertical launch cell carrying them. it is likely that they will carry upwards of 100 of these missiles. These shoot down incoming missiles
5. Last, they will have a Close-in-Weapon System, Probably a couple of 30mm guns for last defense. They too can shoot down incoming missiles.
Once the rail gun is added, they have anti-missile projectiles that will also be very effective.
US Navy ships are the best defended vessels on earth against incoming missiles...but no matter how you dice it, if the enemy finds you and launches, it is a very dangerous thing.
Embarrassing if it is the Iranians or North Koreans that sink the ship.