Open Settings
Tap your name at the top
Scroll down and tap Sign Out
Enter your Apple ID password if prompted
Choose whether to keep a copy of your data on the device
Tap Sign Out again to confirm
Return to Settings
Tap Sign in to your iPhone
Enter the new Apple ID and password
Follow the on-screen steps to finish signing in
If needed, go to App Store and sign in with the new Apple ID
If needed, go to iMessage and FaceTime settings and update the Apple ID there