First of all, you need a bank account. Because of anti money laundering legislation, you'll need proof of identity and proof of address.
After that, you'll need to apply to the bank for a card and they will each have their own criteria. Opening a current account in the same branch as your parents would be a good start.
Think of it from their point of view. How can they be convinced that a teenager will have sufficient funds/income to cover purchases, and that you can be trusted to use the card responsibly, e.g. only spend what you know to be in your account. If you can cover off those types of question, then you're ready to apply for the card.