Face ID replaces Apple's fingerprint tech (Touch ID) to unlock your iPhone and approve certain actions. It takes a little getting used to and you will find yourself going for the non-existent Touch ID button at first.
Once you get used to it you barely notice it is happening anymore. It asks a little bit more security to your saved password too which are now protected by Face ID so if you share your iPhone with someone they won't have access to your passwords.
OK... so how do I use it with Apple Pay?
Again is you are used to Touch ID it can take a little getting used to but works very well once you use it a few times.
It is as easy as 123.
Double press the button on the right of your iPhone