Unloading your trailer
Try not to block any roads (pull as far over as possible so that others can still get by). Do you best to unload quickly, without taking breaks, and move the trailer to the parking area as soon as you're done so that the next person can pull in. You don't need to set everything up as soon as it comes off the trailer; the most important thing is to get that trailer in and out of there quickly once the horses are settled in!
Keep the aisles as clear as possible. Make sure that there's enough room left in a wide aisle for two horses (so that others can pass while you use the cross-ties) or enough for a horse to pass comfortably in a narrow aisle. The more you can keep off the ground, the better.
Keep everything in your own area. You can use the space in front of your own stall fronts, but don't overflow onto others' unless you are invited to. If you have any end stalls, you are entitled to use the space at the ends for storage, too. That end space is incredibly useful, so if you don't plan on using it, it's nice to offer it to your neighbours.
Cross-ties should be located so that any horse using them will be standing within your own area. If you are in a narrow aisle, it's best not to use cross-ties since any horse using them would block the aisle off completely.
Think hard about which horses will use which stalls. If you have an antisocial horse, try putting that one next to your tack stall or in an end stall so that he won't aggravate anyone else. If you are bringing a stallion, inform your neighbours about him and ask for their input on his housing arrangements, too (remember that any neighbours behind will be affected, too). If you have a horse that likes to chew on things, avoid putting him next to anyone's tack stall since some horses are capable of pulling things over the top of those short stall walls.
During the show
Make sure that other horses can pass through the aisle at all times (that means no leaving horses unattended in the aisle). Keep stall doors closed and make sure that any unfriendly horses are kept behind bars!
If you are allowed to bathe horses in the stabling area, make sure that you don't spray anyone else's stalls or equipment. This seems obvious, but when a horse is moving around a lot it can happen accidentally. Also try to keep the water shut off as much as possible or move your bathing area around so that you don't create a big mud puddle. If there are wash stalls available, don't keep your horse in one for longer than it takes you to bathe him so that another horse can use it without too long of a wait.
Leave everything how you found it. If you borrow a hose to water your horses, leave it neatly how you found it (it's usually safe to coil it as tightly as the owners do). The same applies for borrowing mounting blocks. After you've asked to borrow one, either use it where it already is or, if you must move it, ask someone on the ground to return it for you.
Keep the aisle clean. Any poop should be removed from the aisle or wash stall immediately and the aisle should be raked several times per day to keep it smooth and clean.
The busiest time for trailers is the afternoon of the last day of the show because everyone wants to leave at the same time after the classes finish. Prepare by packing all of your things up in the morning so that everything can be loaded at once, without delays. Again, try to load quickly and then get out of there to make room for others.
If you are not comfortable navigating your trailer in tight spaces, don't attempt to pull up close to the barn during the busiest times because you might end up blocking others when you can't get back out! If you can't pull in nearby, try loading your things onto the back of a truck and then taking a few loads out to your trailer that way. If you have time, it can be much easier to just wait until your neighbours have left and then you can load at your own pace.