How can I download an app without a credit/debit card

You can download free apps, but you may need to have a valid payment method on file, even if the app you want to download is free. 

Free apps has also In-app pruchase.

See also -> Buy additional app features with in-app purchases and subscriptions

Buy additional app features with in-app purchases and subscriptions

You can have a credit card / debit card on file and an Apple Account balance.

If you have set your Apple Account balance as your default payment method, your default payment method will be used first by Apple when you need to make a payment.

If you don't have a credit card or don't want to use a credit card, you can also use your Apple Account balance as payment method.

See -> What you can buy with your Apple Gift Card or Apple Account balance

What you can buy with your Apple Gift Card or Apple Account balance – Apple Support (UK)

and ⤵️

• You can't use your Apple Account balance to send gifts or gift cards.
• If you use Family Sharing, your family members can't spend your Apple Account balance. Funds that you add to your Apple Account balance are only available to you. Find out more about how purchases are billed to your Apple Account balance.
• Some purchases might require you to have a credit card on file, even if you use your Apple Account balance to make the purchase.

See also -> Apple Media Services Terms and Conditions -> Legal - Apple Media Services - Apple

See -> Add a payment method to your Apple ID

Add a payment method to your Apple ID – Apple Support (UK)

•  if you want to use your Apple Account balance, you need to set your Apple Account balance as your default payment.

If you have a valid payment method on file, instead of buying or order an App Store & iTunes gift card, you can Add money to your Apple Account balance anytime, no gift card needed, see -> Apple Gift Card - Apple (UK)

Where to buy a physical Apple Gift Card or App Store & iTunes gift card: actually, you can buy an Apple gift card at many places, at an Apple Store or an Apple Authorized Reseller in your region.

See also this Apple article:  If you can't redeem your Apple Gift Card or App Store & iTunes Gift Card

If you can't redeem your Apple Gift Card or App Store & iTunes Gift Card - Apple Support

Beware of -> About Gift Card Scams -> About Gift Card Scams - Official Apple Support 

If you still need help, get support from Apple directly -> Get Support or call Apple in your region see -> Contact Apple for support and service or check -> here for more support and assistance.