Just by chance really. Mine is based at another yard I looked at when I moved earlier this year. Did a bit of googling and decided to give it a try. I had to find someone local as I have no transport so was a little short of options... has turned out really well though and we have made great progress with her
From the other side of the coin - I'm a dressage trainer, some of my clients have come through here, some through British Dressage, a lot from word of mouth and I also advertise and have a Facebook page and a website. (www.facebook.com/parisiennedressage - there is a link to my website on my Facebook page).
I do have trainers that I go to, one of which is a top International dressage rider, the other I met via competing (she is at a higher level than me) and I really liked the way she rode and trained so I started having lessons with her. She also has a very good reputation which is really important to me.
I have found all past instructors through word of mouth (often seen them advertising too so I would know of the name and a bit about them anyway) I have a list of top riders who I would potentially have a lesson with due to the way they ride when I've seen videos of them online, and others I would definitely miss! An ad alone isn't enough for me, I want to know about their approach and ethos, do they teach only to fund their competing, or do they teach because they actually want to inspire others and are passionate about the welfare of the horse.
Most of my clients have found me through word of mouth and recommendations, although I do have a website and I advertise locally. I would want potential clients to connect with my approach and like what they see before they even had a lesson.
My YM found ours when he judged her in a dressage test. She went over and asked him how she could improve and ended up booking a lesson with him. She then recommended him to most of the yard