> I wanted to learn exactly what happens in the ring from start to finish
The steward will call your class, be ready, standing by the opening, dog all groomed, show lead on, treats ready if you're using them, brush ready if needed.
So you enter the ring when the steward calls your class, you may already have your number in which case it's attached to you, or the steward may give you it, if collecting it from the steward I put it in my pocket for the moment and attach it once the judge is going over another dog.
I like to get at the front of the line up, for psychological reasons, I want the judge looking at my dog, he's first, looking good and setting a good example, keep him first

I also want to set the pace when or if we all move round together.
When you're just new though and maybe not that confident try and be in the middle of the line, not last, you want time to get your dog ready when the judge has gone over the last dog and is starting to sort them in their mind.
Don't chat to other exhibitors or people outside the ring, pay attention to your dog and the judge and steward. Set your dog up straight away, the judge will probably be at the table, maybe blethering, waiting for the steward to say that's everyone. During this time though they will often look over, you don't want your dog standing with a leg out of place which can make them appear to have a fault they don't actually have.
The judge will either indicate for you all to run round together or the first dog to come up. If you're all moving together leave enough space between you and the dog in front and keep an eye on the judge. If you're getting too close to the dog in front slow down for a few seconds when the judge isn't looking at you and be sure to go your dogs ideal speed when the judge is looking. This is easier than it sounds as most judges stand looking at one long side of the ring, so you can slow down on the short end, give yourself space then move out properly when it's most important. Always have your dog on the judges side, they don't want to see your legs. It's not polite to overtake fellow exhibitors, though I have seen it done, better to just slow down, or turn in a circle.
Once you've all moved round the ring once or twice, whatever the judge wants the first dog will go to either the table or in front of the table to be set up for the judge. You can let your dog relax at this point but still be aware of them. I have a coated breed so I don't want them lying down and maybe getting cut grass in their coat. I also don't want them standing facing the judge unless I'm sure their front legs are straight, I'd rather they relaxed side on to the judge.
Watch what is happening, usually when the dog in front is moving the next dog can go forward and take that time to get ready before the judge looks round at them. If you're not sure about anything ask the steward.
Only speak to the judge if they speak to you and only answer their questions, usually just 'what age'. If it's a pup/junior answer in months, if it's an adult dog answer in years, generally rounding down until you get to veteran then you can round up. So a 2 1/2 year old is just 2, but a 8 1/2 year old could be almost 9.
Don't feed your dog just before the judge checks their teeth, you don't want bits of food sticking to them. Once the judge has looked in their mouth you can bring a treat out to keep the dog looking forward while the judge goes over the rest of them. Try not to get in the way of the judge, but don't be afraid to correct a leg if a judge moves one and it doesn't go back into the right place.
When asked to move make the most of the ring, use all the space there is. Don't be afraid to turn round and start again if your dog isn't going well, is scratching, pacing, jumping around or something else that isn't showing their best movement. If they're being really naughty though sometimes you just have to make the best of it, you can't restart 17 times, in fact I would restart no more than twice, and I'd probably apologise while doing it.
When you come back from moving stop a few feet away from the judge, don't run right up to them, turn your dog side on, allow them to stand naturally, unless they look really awful then move round in a circle and try again.
The judge will then either thank you and look away to the next dog or ask you to join the end of the line, in either case keep showing your dog until you get to the end of the line, trot round and gt your dog to stand at the end. Once you're sure the judge has looked away your dog can relax again.
You don't relax though, pay attention to the line, specifically who was first. Once the last dog goes up to be gone over you can get yours ready again, maybe he needs a quick brush, then when the last dog is moving get yours standing.
You want to keep your dog standing now while the judge makes their decision, watch the judge but remember they can see you too, sometimes people are so intent watching the judge they're actually glaring at them

you want to look quietly confident.
You'll have seen in previous classes how the judge is placing them, either from 1 back or starting at the low end. When the judge points to you move out into the middle of the ring, the steward should indicate where you should stand. If you didn't win always congratulate those in front of you, just a quick well done is fine. Depending on what you've won you may have to stay there for the judge to write a critique on your dog, keep them looking at their best for this. If you haven't been picked and you're sure all places have been filled just pat your dog and leave the ring.
We've all had embarrassing moments in the ring, don't worry about it and don't be afraid to ask the steward for help. I've been showing for decades, have made champions up and still get embarrassed in the ring. Either with a young dog who forgets all it's training or more recently when I was showing in Germany. I don't speak german, I watched the judge placing all classes from 5 to 1, we won open dog and were in for the challenge. The judge pointed to someone else, said something in German, the other handler squealed and trotted over to the reserve spot, or at least that's what it looked like to me. Then she pointed at me, I assumed we had won the ticket and went over to that pile of prizes to a shocked silence... the other lady was winners dog/cac but had knocked over something on the reserve spot on the way past and stopped to pick it up. Oops, where is that hole in the ground!
Anything else?