What age do I need to be to use Apple Pay ?

The only requirement, is that the Apple ID being used, have a minimum Age of 13 or over set for it.

If you are over 13, and have a supported debit or credit card, you can use Apple Pay.

Read here for details:

Set up Apple Pay - Apple Support

If you are referring more specifically to Apple Pay Cash, then you need to be 18 years or older to make use of it.

More details here:

Set up Apple Pay Cash and person to person payments - Apple Support

Small addition to Phil0124's post.

This is not just Apple's requirement. It can also depend on the country you live in. In the UK I don't think you can get a debit or credit card under the age of 16.

Other countries may differ further.

As Phil says, you need a card to support Apple Pay; I am only clarifying the national legal requirements.