After the introductory cutscene, you'll find yourself in your room. Head downstairs and speak with your Mom. She'll give you a Town Map. Exit your house and head north to meet Bianca, Professor Juniper's assistant. She will present you with a briefcase containing three starter Pokémon: Snivy, Tepig, and Oshawott. Choose wisely, as this Pokémon will be your first companion!
Once you've made your choice, Bianca will also give you your very own Pokédex, an invaluable tool for recording information about all the Pokémon you encounter. She'll then instruct you to meet Hugh, your childhood friend and rival, who is waiting on Route 19. Before leaving Aspertia City, consider visiting the Pokémon Center to heal your Pokémon and stock up on any essential items if you have money, though you won't have much at this point. The Pokémon Center is always a good first stop in any new town.