Welcome to the Apple Community.
To be able to download free apps without a recognised method of payment or gift card.
Open iTunes and navigate to the app store. Select a free app to download. A simple way to do this is to scroll down to the top free apps box on the right hand side, hover your mouse over the first item and click on the free button that appears when you hover over it.
A pop up will open asking you to sign in with your Apple ID click "create new account", click continue to create your account. Check the box to accept the store terms and conditions and click continue.
Enter your email address, password, security question, and date of birth, click continue. Now, you will be asked to provide a payment method. Note now that the last option says "none".