There really isn't a "correct" way per se, but it was more or less a discussion on when it's appropriate to say things.
But I think it's a learning process.
Like I don't give runway or wind information any more because people really don't care.
"Ooh, westerly winds on 35 center grandma!"
But I will give them information if we're landing to the north or to the south if someone's hankering for a glimpse of something notable on arrival.
I don't give out the flight number after the door closes. Passengers already know it's flight 12345 and know they're going to Sacramento. This is something I typically might do on a Salt Lake City to Sacramento flight:
Good afternoon from the cockpit, this is first officer Doug Taylor...In command of your aircraft is captain Joe Jackson. We've just reached 33,000 feet and if you look out to the right, you'll see the Bonneville Salt Flats, a little later, our route of flight will take us over the sierra nevada mountains near Yosemite and we'll begin the descent over (whatever is near the descent point). As we said earlier, the time enroute is one hour and eleven minutes, which should have us touching down at noon and into the gate shortly thereafter.
Captain Jackson thinks there might be some choppy air along the route of flight so if the fasten seat belt sign comes on, please make sure you return to your seat and check the security of your seat belt.
The forecast weather at our arrival is indicating 15 degrees centigrade, 59 degrees fahrenheit, light winds and clear skies and that should continue for the duration of the day. We've got a Cincinnati-based cabin crew and they'll take good care of you. We invite you to make yourselves comfortable and we'll do all we can to give you a safe, comfortable ride to Sacramento.
Enjoy your flight and thank you for choosing Delta
I don't always use the same PA and I change the words often so I don't get bored and start talking like a auctioneer.