How to start a new game of The Legend of Zelda: Phantom Hourglass.
Choose a new game slot from the main menu, or select an existing save file and choose Erase, then tap the new game slot in the main menu.
Enter a name, then choose whether you hold the stylus in your right or left hand.
Then in the file selection menu, tap the game slot that you created, and tap Start.
You will be prompted to choose Adventure or Battle.
About Battle Mode
The Battle mode is a multiplayer mode that you can use to play against other nearby players who have a Nintendo DS or 3DS. Select Multiplayer to play against someone who also has the game. Select DS Download Play to play against someone who does not have the game. The Nintendo WFC mode is no longer available.
You can tap How to Play to learn how to play multiplayer mode. You can tap Change Name to change the name that appears for you in multiplayer mode (but this does not change your name for Adventure mode).
In the screen where you can choose between Adventure mode and Battle mode, you can tap Options to change the message speed, sound settings, hand setting (left or right) and do a Mic Test to make sure that your microphone is working (since it is required for some puzzles in the game).
When you are ready, tap Adventure, and your adventure will begin.
There will be a cut scene. It contains spoilers of The Legend of Zelda: The Wind Waker. If you want to skip it, you can press Start, then tap Skip on the touch screen. You can do this to skip any cut scenes in the game. Be sure to skip these first cut scenes if you want to avoid the spoilers. However, cut scenes later in the game may also contain Wind Waker spoilers.