On the ground training and then undersaddle. When I broke babies how we did it.
Turn on the forehand, moving the shoulders (not turn on the forehand or a walk pirouette), go, stop, reinback, and leg yield are all things I like to teach a new horse within the 1st month undersaddle.
Shoulder in then Travers (haunches in), renvers (counter flexed haunches in), half pass then pirouettes.
Note: A walk pirouette is ridden with all 4 legs leaving the ground. The foots must NEVER stick. So a lot of times when I train and school a walk pirouette, I rarely school on a tight pivot, Usually larger and more like a half pass on a circle. Similar note a canter pirouette is done in 4 beats. I have seen people say online, it should be 3- no NEVER 3. if it is 3 it is very poorly executed and ridden. Why most people when schooling pirouettes school on a large circle and do not school on the spot very often. The goal is to keep the right mechanics. How things are schooled at home is not how they are ridden in the show ring.