How do I add a payment method to my Apple account?

This document explains how to add a payment method to your Apple ID on a Mac, Apple mobile devices, PC, or online. Click here --> Add a payment method to your Apple ID - Apple Support

On an iPhone:

Open the Settings app.

Tap your name.

Tap Media & Purchases, then tap View Account. You might be asked to sign in with your Apple ID.

Tap Manage Payments.

Do you mean all the ways listed in the document I provided do not apply to what you are using? I just posted about iPhones because that's what many people use. The document which I invited you to read lists many more ways. I suspect you could even be using a Cary supercomputer, assuming it can connect to the internet and has a web browser..