Horse showing help..?

No, you should not be trotting. You should enter the ring at a walk tracking left. Once all of the riders have entered, you will be asked to trot.

Some people like to get a good position on the rail by trotting past all the other riders who are walking. Personally, I don't like to see people do that and I've never done that. If there's a group of riders that are all bunched up, you are allowed (and encouraged) to pass or to circle to the other side of the ring so that you are by yourself. But don't trot past a bunch of walkers.

If you are doing any jumping, enter the ring at a walk and quickly pick up your trot. Trot a quarter of your warm up circle, then canter the other 3/4 of the circle and continue to your first jump.

Definitely don't trot in! Usually the previous class will be lined up in the center of the ring, so when the gate is opened, line up with the rest of the people in your class, and file in. Try to find your own spot in the ring, circling, or passing (at the walk). Although you aren't being judged at this point, you should make sure you're still polite to other riders. Try to avoid horses of a similar color, and when you line up to be pinned, loosen your reins, as the judge wants to see that your horse can stand on a loose rein. Also, make sure you know what kind of class you're in! Pleasure, discipline, and eq. are usually the classes included in a division.

I've never shown, however I do ride english. My suggestion would be to youtube-search some classes or attend some shows of the same discipline/class you will be showing in. See if your show has a rule-guide, or ask someone you know that might know the show well. If you have an instructor or if you board with someone, try asking them.