The Royal Unova is a boat found at the dock by the Pokémon Centre in Castelia City. Until you beat the game, you cannot access this boat. However, once you have received the National Pokédex, you will be able to access it. The Royal Unova sets sail once a day, with it's sailing time varying between season.
It costs you 1,000 PokéDollars to get on. However, there is a catch. There is a time limit to being on the boat. Once that time limit is passed, the boat redocks at Castelia City and you get given an item based on the trainers you defeated