Learn the turn on the forehand: how the hindquarters yield to the leg without the horse stepping back or rushing forward, calmly, clearly and without force.
Why should my horse step sideways with its hindquarters? The honest answer: because the turn on the forehand is the simplest exercise in which your horse yields sideways to a leg instead of only running forward. You learn to use the leg precisely, and the horse learns that leg pressure can mean "yield to the side".
I found no study specifically on the turn on the forehand. That is partly because it does not appear in the FEI dressage rules I read: they regulate its counterpart, the turn on the haunches, and the pirouette [1]. So the exercise is riding-school practice, not a competition standard. I therefore state clearly what is evidenced and what is practice.
What is evidenced is the learning principle: horses learn rider aids through pressure and release, and the release must be prompt, consistent and easy to achieve [2]. Constant pressure risks dulling the aids. For the turn on the forehand that means: one step, praise, pause. And another finding: in the FEI rules leg-yielding counts as an important preparatory exercise that belongs in training before the horse shows collected work [3]. The turn on the forehand is a gentle preliminary stage for it.
Stand the horse straight and parallel to the boards at the halt, head toward the boards. Leave room for the hindquarters so they do not bump the wall. Milestone: The horse stands calmly without pawing.
Apply the inside lower leg a hand's width behind the girth for a short impulse. This is riding-school practice. At the same time the outside hand limits lightly so the horse does not run forward. Milestone: The horse stays standing and lifts the hindquarters one step sideways.
As soon as a step comes, you take the pressure away at once and praise. It is exactly this release that makes the exercise understandable [2]. At first ask for just one step. Milestone: Your horse steps sideways on a light impulse and then waits.
Gradually build in more steps. After each step pressure off and pause. The clearer the signal, the less force you need. Your goal is small, calm steps, not a fast run-away of the hindquarters. Milestone: The horse makes four to six steps without moving the forelegs far.
End the exercise with a calm walk-on. For the pirouette the FEI requires that the horse stays active and never moves backwards or sideways [1]. I transfer that as an idea to the exit of any turn. Milestone: Your horse walks on calmly without stepping back.
The turn on the forehand does not replace supervised training. As a beginner practise it only with an instructor. The horse may tense up or evade under pressure: the FEI names tongue play, teeth grinding and tail swishing as possible signs of nervousness, tension or resistance [4]. These signals are not proof of pain, but they are a reason to stop. Never force the horse with constant pressure or a whip: the FEI requires that horses are not subjected to methods that are abusive or cause fear [5]. Mind your horse's hindquarters: do not stand directly behind the horse when you help from the ground. In one study hoof kicks mostly led to facial fractures [6].
Practise the turn on the forehand first from the ground: stand beside your horse's hindquarters, tap lightly with the hand behind the girth and reward one step. That way your horse understands the pressure already on the ground. This is training practice; there is no study for it. Mind safety though: only with your instructor and with a lateral distance from the hind legs [6].
In the turn on the forehand the hindquarters step around the almost stationary forehand; in the turn on the haunches the forehand turns around the stationary hindquarters. The FEI calls the turn on the haunches an exercise that prepares younger horses for collection [1].
In the FEI dressage rules I read it does not appear; the turn on the haunches and pirouettes are regulated [1]. So it is a classic riding-school and training exercise.
Start with one step and increase only slowly. More important than the number is that the horse stays calm and you take the pressure off after each step [2].
Do not increase pressure but make the aid clearer: short impulse, release at once, ask your instructor for help. Constant pressure dulls aids and makes horses unhappy [2].
It trains your feel for the sideways-driving leg and is a preliminary stage to leg-yielding, which the FEI names as preparation before collected work [3]. The sources I read prove nothing beyond this classification.
Rein-Back: Stepping Back Calmly Without Hauling on the Rein