you just need your name to be out there!! my trainer is a grand prix rider who is in a lot of the big shows so since i train under her, she sort of "advertises" us (clients) and sometime people ask us to show their horses. the key is to have the platform (known trainer, big instagram acc, go to big shows a lot, etc.). if you're just starting i also reccomend seeing if owners AT your barn would like you to catch ride their horses @ a show. i love catch rides bc it's literally a free show, which in my family is a big deal since this sport is so expensive!!
Definitely learn to count your strides in between jumps and use your body and not pull the bit too much