Take them everywhere with a reliable horse! Start small and develop into bigger shows
I always try and take them to smaller shows to start off with and as they get used to it start taking them to bigger shows
I would first of all practice taking your horse to a new place that isn't during a show so they could get used to traveling. At the shows you could try multiple things, getting on early and walking them around until they relax, hand walking them around the property before you ride, lunging them, or give them calming supplements.