First of all, most people I know purchase a double cage space. And you only bring your own cage if you have one of those sturdi-cage nylon pop up ones. The show cages are large enough, and for your first show you can just bring about 4 towels to use as curtains.
The cage has no bottom and a top that flips up. You lay down a towel under the cage, and then line the back three sides. Then you flip the top closed, and it's best to clip the top with large paperclips. A towel is then laid over the top to complete the cage curtains and shield your cat from all the cats around him. They feel safer when enclosed on three sides. There are two doors in the front of the cage, and you use those to take your cat out.
It's best to teach your cat how to be removed tail first as that is the way the judge will remove him from the showing cages when it's his turn.
When you enter, you can put a note on the application saying that you are new and that you want to be placed with an experienced shower. And when you get there, you can tell the entry clerk that it is your first show, and they can set you up with a club member who can show you the ropes.
I have shown three times total, and the first two were very nerve wracking. It gets easier, and people are forgiving of mistakes.
Your cat gets a number, and the show will generally follow a posted schedule. There will be a lot of exceptions however, depending on how fast the judges work, and cats may be called to two different rings at the same time. The schedule is flexible. In the showing rings, there are place holders above each cage. You keep an eye on them, and when your cat's number is put in the place holder, you put your cat in that cage, then sit down and watch. It really is easy once you get the hang of it.