How do you set phone so screen is not always lit up?

The screen locks either manually or via Auto-Lock in Settings. You can manually lock the screen with the side button, or automatically by going into Settings>Display & Brightness>Auto-Lock, and set the time you wish to pass before the screen goes dark and locks.

Adjust the AutoLock time option in Settings>Display&Brightness.

When done, restart your iPhone and test it.

Regards

Giulio