Get to the Dome before the doors officially open (usually 1.5 hours before "game time" so you can walk around the building and explore as many areas as possible. Check out all the FanAttic shops because they can have different items. There's also some displays around the ends to look at which are new after the flood.
Then make your way to section 102-103 before 7:30 and get yourself a front row seat for the warm-ups. You can sit anywhere that's open so long as you politely move if the actual ticket holder for that seat shows up. The view from 102-103 is the best for the Flames warm-up. Admire the size and speed of the players. You could even try for a selfie when guys are lined up along the glass while running drills. Just don't bang on the glass like a moron.
Don't feel rushed to leave the second the buzzer sounds. Hang out for a bit and experience the Dome after the game. Eventually you will have to go but you don't NEED to rush out the door with 15,000 others all at once.
If you have no real plans after the game head out the East exit doors on the right side of the interior FanAttic store and go to the bottom of the stairs. To the right is the entrance to the players parking lot. You can hang out there along the fence, as guided by the lot attendants, and players usually stop and sign autographs after the game. It will be 30-45 minutes after the end of the game before players slowly start coming out and can take 2+ hours after for every last one to leave. But meeting some of the team is an experience you won't soon forget. Just be polite and courteous and if you'd like a photo ASK them if it's ok first. If you are interested in doing this make sure you go to the bathroom before you exit the building, have some warm clothes and know where you are when it's time to leave. The East side is a long walk around the building to get to the train or to find a cab if those are your modes of transportation.
I'd also suggest if you have a jersey you do want signed in a black area that you stop by Walmart or Michael's and pick up a silver paint pen first. Silver Sharpies will not write very well and fade easily. Paint pens are forever. And have the player personalize it. Anyone can have a Sean Monohan signed jersey. Only YOU can have a Sean Monohan jersey personalized to you.
Between 102 and 103, best place to go to watch warmups. Walk down to the glass and have a seat.
https://www.google.ca/maps/@51.03694...7i13312!8i6656
East exit
https://www.google.ca/maps/@51.03755...7i13312!8i6656
Outside with stairs down to parking lot. Then you go to the right (behind the temp building)
https://www.google.ca/maps/@51.03759...7i13312!8i6656