You can purchase your child membership to Club Penguin Island through the following steps:
1. Tap the About Membership button on the main menu.
2. Tap Confirm Free Trial. (If you've already been a member, the button will be called Membership).
3. If you're not logged in, enter the Disney Account username and password used for Club Penguin Island. (If you're already logged in, you'll automatically skip to the next step).
4. Select your age.
5. Tap Confirm Free Trial.
6. Confirm your iTunes password when prompted.
7. Tap Continue to confirm your purchase.
Woohoo! Your child is now a Club Penguin Island member. They'll be able to wear their custom styles, take part in Adventures, and gain access to exclusive items!