How can I share my payment method?

If you mean your Apple Account balance, you cannot. Normally once funds are in Apple Account balance the only way to get them out again is to spend them.

From: Check your Apple ID balance - Check your Apple Account balance - Apple Support -->

"About unused Apple ID balance

You can't redeem or return Apple Gift Cards, App Store & iTunes Gift Cards, or unused Apple ID balance for cash, except as required by law. If your jurisdiction allows for refund of redeemed gift balances, you can contact Apple Support."

If you mean your credit or debit card, see if you can enter it as a payment method. This document explains how to add a payment method to your Apple ID on a Mac, Apple mobile devices, or PC. Click here --> Add a payment method to your Apple ID - Apple Support

If that doesn't work, consider setting up Family Sharing with you as the Organizer. Your payment method can be used to pay for the purchases of the other person. To learn how to set up Family Sharing, read this support article --> Set up Family Sharing - Apple Support