The details you need should be in How to pair your Apple Watch with a new iPhone - Apple Support
I had to do something similar when my old iPhone fell into deep water. Fortunately I had a recent iCloud backup of the iPhone. When I setup the new iPhone (still in the Apple Store) using the same Apple ID it offered to restore my backup data. This detected my Apple Watch and offered to set it up. Everything just worked, all I had to do was respond to a confirm code to restore my ApplePay on the new phone. The whole process needed less than 1 hour from walking into the store, to walking out with a fully configured new iPhone. The only delay was synchronising my photos collection back from iCloud storage which completed overnight.