You can test your Apple Pay on the Web integration using a real card and your test API keys. Stripe will recognize that you are in test mode and will return a successful test card token for you to use. You can read more about testing your integration in the Stripe Docs.
Note: Apple Pay on the web only works on Safari web browsers, both desktop and mobile.
Once Apple Pay is set up to be used on mobile iOS devices, you can use your test API keys in your application to initialize Apple Pay. You will need to enter a real credit card number to your Apple Pay wallet, as the wallet does not allow Stripe's test cards. However, if you are in test mode and using your test API keys, Stripe will tokenize the real card to the fake test card and you can move forward using that for testing.
Note: You can test your Apple Pay mobile integration using an iOS simulator as well as on a physical iOS device.