The Royal Unova is a boat found at the dock by the Pokémon Centre in Castelia City. Unlike in Pokémon Black & White, you can go on the boat straight away, as soon as you enter Castelia City. 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