Note that Apple now offers its own credit card native to iPhones and easily usable with Apple Pay.
Once your card is set up, paying with Apple Pay is intuitive. Hold the iPhone up the the point of sale terminal, and use Face-ID or a passcode to approve the purchase.
Find more detailed instructions for setting up Apple Pay here.
You can also use Apple Pay on an Apple Watch, once you've set up a card on your phone. It works nearly the same as on the iPhone, and is activated by pressing the side button to bring up the primary card.
Find more detailed instructions for setting up Apple Pay on an Apple Watch here.
Add a credit or debit card in the app, and be sure to select "Set up in-store payments."
Find more detailed instructions for setting up Google Pay here.