I am having trouble adding a payment method. How can you fix this problem?

What happens when you try to add the card? Error message(s)?

See the Apple Support article(s) below. Link to contact Apple Support in the article. 

Apple ID payment information - If your payment method is declined, or you have a billing issue with a previous purchase in the iTunes Store*

Possible fixes.   Fix ‘Your Payment Method Was Declined’ Error In App Store.  -

                          Payment method declined in iTunes or the App Store.   -

If necessary, contact iTunes Support for assistance. See the Apple Support articles below for contact information.   

iTunes Support – world wide   -

Apple Support schedule phone call     -

Billings and Subscriptions   -

Apple on Twitter

Sign in to your Apple ID account page and edit your Apple ID details.

https://appleid.apple.com

On the Sidebar click Payment methods -> then tap Payments Methods and tap Manage payment method.

See  also the following Apple articles:

Change, add or remove Apple ID payment methods

Change, add or remove Apple ID payment methods – Apple Support (UK)

Add money to your Apple ID balance

Add money to your Apple ID balance – Apple Support (UK)

Payment methods you can use with your Apple ID

Payment methods you can use with your Apple ID – Apple Support (UK)