From Bulbapedia, the community-driven Pokémon encyclopedia.
When you begin the game, you will be asked if you are a boy or a girl. Be careful, as this cannot be changed later on. Then the game will begin and you will find yourself in the skies of the Oblivia region.
Flying Above Oblivia
You start out by seeing some Pidgey, but they get frightened and fly away. Then either Latias (if you are a girl) or Latios (if you are a boy) flying at amazing speeds away while being chased by two people with strange energy cannons. As they are chasing it, you hear a Staraptor's cry and they turn around to see you come speeding in. They recognize that you are a Pokémon Ranger, so they send out a Pidgey. This is a nice easy capture to get you started: just use your stylus to draw circles around the Pokémon.
Then they decide to shoot at you. Use the touch screen to make Staraptor dodge the blasts. Then they are about to ram you, but fortunately your partner (Summer if you are a boy, Ben if you are a girl) comes along and scares them enough to make them think about retreating. But then Red Eyes comes along at shoots at your partner. Then you fly in and take the blasts for your partner, and are sent hurtling down into the ocean.
In the Ocean
When you land in the ocean your styler detaches from your wrist before a Mantyke takes it and swims away. You then chase after Mantyke. Use the touch screen to steer and avoid attacks and touch the player to speed up once the red bar has turned green. When you catch up to Mantyke and retrieve the styler, you then wash up onto Dolce Island.