A big thing to consider is doing a fecal at least a couple of weeks before to ensure there are no parasites/cocci, because that will really hamper their health. Depending on your location if it's been wet and humid like it has been here, then cocci is one to worry about. Make sure they are healthy going in - good weight, no eye/nose discharge, eating good, etc. You can add Gatorade to a bucket of water or electrolytes (Bluelite is great), that away they get used to drinking that and when you go to fair you can add it to their water and it won't taste so different to them. Sometimes goats don't drink well if the water tastes different, so masking it helps.
Probiotics and oral B-Complex helps with stress.
If you are able to wash your goats before going home, then that is best, or try to use some kind of fungal spray on them after they leave the show ring. I am guilty of not doing that the last couple of years, but normally we would spray everyone down with diluted bleach water, especially legs and feet and topline. But they make spray products that make it safe and easy.
Give probiotics day after show, especially if they have been stressing. Otherwise all you can do is really just watch, get them back into their routine and comfortable.