Early reservations at the Specialty restaurants are often at half price. It's not difficult to reserve a table at them, but may be difficult to reserve a table at the Teppanyaki table, that doesn't sit many. You can use the phone in your cabin to make a reservation, make one at the atrium area, or at the restaurant.
Lately, NCL has changed its policy for reservations, being only able to book a table for that night and the following night, so the rush to reserve a table on the very first day is over. But now, the rush is every morning.
It's easy, the sooner you reserve a table, the more choices you'll have.