From Bulbapedia, the community-driven Pokémon encyclopedia.
When you begin the game, you will be asked if you are a boy or a girl. Then the game will begin and you will find yourself in the skies of the Oblivia region.
Flying Above Oblivia
You start out, flying high above the region of Oblivia. You see either Latios or Latias (depending on whether you're playing as a girl or boy) being chased by strange people on weird flying contraptions. It's revealed that you are a Pokémon Ranger on a special assignment.
The strange people attack you with Pidgey, which is your first capture. Draw loops around it, avoiding its attacks, and once its Friendship Gauge is full, you've succeeded.
After a successful capture, the legendary Pokémon will escape, angering your enemies. They shoot at you with plasma cannons, so dodge quickly.
At this point, Summer or Ben will join you. However, the enemies' leader appears and readies himself to attack your partner, and to protect your friend, you throw yourself in front of them and end up falling into the sea.
In the Ocean
When you land in the ocean your styler detaches from your wrist before a Mantyke takes it and swims away. You need to retrieve it. 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. It uses Bubble which causes 1 damage. Retrieve the styler, you'll get a message that something big is headed your way. You feel the rumbling and are washed away by a submarine.