Maura pretty much got it.. Hunters is pretty simple. It's all about who you know, which is why I don't like it sometimes. You don't get all the politics and crap with eventing....
Anyway, I've ridden hunters for years, and even though I haven't really started getting into it now, I think I pretty much know the ins and outs of it. Also, it completely depends on the type of show. Low-key schooling shows, some of this isn't as important. If it's a county/regional type show, you might be up against some really high quality horses and, speaking from past experience, regardless of what you do you'll feel a bit out of place. But as a general rule, this is how hunters are. Hopefully it doesn't sound too elementary, but I'm not sure how much you already know. For a jump course: Walk in at the walk, pick up a trot, and do your courtesy circle. (Depending on the way the course is set up, you may not need to do one. If you start coming towards the gate, then you can omit it. Just see what everyone else does.) About halfway through your circle, pick up a nice relaxed canter. When you go to the fences, make sure you have nice approaches with long sweeping turns. It's not about time, you want it to look nice and smooth. Take your time coming up to the jumps. Don't rush, and find a good spot. As maura said, leads and strides are important. Count your strides heading down the lines, and if possible switch your lead over the fences. (Flying changes are better than simple obviously.) Simple changes are allowed, but you'll get nicked for them, especially once you get in the 2'6''+ range where you're competing against potentially reallyyyy nice horses (I competed against a 17.2h $70k mare last winter. Yes, $70k. Made my $3k pony mare look like a pile of garbage...) Don't forget your courtesy at the end of the course too. If your horse is like mine and has a better trot than canter, it might help to break to the trot for most of the circle so the last thing the judge sees is good.
For the hack classes, remember hunters is all about long and slow with a nice big stride. Typically you have about a minute in the ring before you're actually judged, so when I go in I trot up to a nice open space away from everyone. If your horse goes better after cantering a couple strides, feel free to canter. Just make sure you have a show-quality walk in a good spot by the time the announcer says you're being judged at the walk. Good eq in the hunter world means head up, shoulders squared, chest open, with your leg correctly aligned and heel below you. Depending on the judge, they may be picky about certain things. Some are sticklers for having your thumbs on top, others like a more forward seat, etc. If you can watch who they pin in the earlier classes and tweak your style for your classes. For your horse, resist the urge to put her into a dressage frame. I event too, so I know how tough that can be sometimes, but you'll get penalized for it. You want her to stretch down into the bridle and relax. And remember, consistency is key. The more steady your pace, the better. You want it to look easy. Even when your horse spooks at the invisible monster in the corner, or takes a 2' vertical like it's Mount Everest, you want it to look like you're having the time of your life and your horse is a perfect angel. Don't be afraid to smile!
Hopefully this is helpful. If you have any other questions, feel free to ask :)
Worth The Wait <3