Many dressage riders I know can tell you a story about the time they first rode a well executed lateral movement on a proper schoolmaster.   It is, for many, an experience that hooked them into a lifetime pursuit and activity...   A lifetime of dressage.
For many riders, lateral movements can seem daunting at first.   However, when boiled down to the basics, every horse handler is probably doing some lateral work with their horses without even knowing it.
Within a hour after birth, a newborn foal learns about lateral movement.   His (or her) dam will teach him to move sideways on a very light suggestion.   He learns to move away from her pressure, thus performing his first lateral movement.
In its simplest form, lateral movement is about moving sideways.
Some lateral movements are done with very little bend through the body, some are done with a good deal of bend.   Some are done with the horse facing the direction in which he is moving, some are not.   But boiled down, they all have this one thing in common.   Moving over.
The first lateral movement trainers teach the horse is the same one his dam taught him.   Move over!   We teach this from the ground and can practice it in the stable, while leading, while tied, before mounting, and when moving him to and from the pasture.
One of the first "move over" commands will be to get the hind end to swing away from us.   This is the basis of the movement known as Turn On The Forehand and is where the front end pretty much stays in one area while the back end swings around.
Another "move over" command is where we ask the front of the horse to move away, not really worrying about the back end.   When the hind end stays in one area and the front end moves over, this is a simplied version of a Turn On The Haunches or Pirouette.
When the "move over" command is for the whole of the horse to move sideways, you are actually asking for a Leg Yield or Side Pass.
So, long before we ever get in the saddle, we teach lateral movements from the ground.   And, by putting pressure where we will later put our leg, we are teaching the horse a basic aid for lateral work.   When we later get in the saddle, we aren't teaching the horse something totally foreign to him.   His learning experience is made easier this way and his chances of success are higher.
We like to teach lateral movements to a horse in a logical sequence.   The ladders for lateral movements look like these:
|Move over||We accept ANY positive response to give way to pressure.|
|Turn on the forehand||Staying safely near the horses head, we ask the back end to move over a bit.   One step is good enough and reason to praise the horse.   In fact, one step is much better than the horse running away from us, trotting his hind end around in an attempt to escape!   We want a calm response to the request.   Just move over one step.|
|Turn on the haunches||Staying near the neck, we push the horse to the side, finding his sweet spot to which he best responds, asking him to step away with his front legs.   This is simply "yielding the shoulder" away from our pressure.   Again, one step at a time is good progress.|
|Turn on the forehand||One step is all that is needed.   However, it is not so easy as that, as the rider is no longer able to hold the horse by the halter while asking for the movement.   So, one has to really take their time here.   The horse has to learn to not run forward when we ask for one step of "move over".|
|Leg yield back to the rail||Once training has begun, we can use the horse's desire to stay on the rail, wall, or track.   Coming away from a corner onto the long side, we turn one step early, walk forward a few steps, say "Move over", and give a nudge with the inside leg right where we were giving it when we did this from the ground.   A step of leg yield is all we want at first.   As confidence in this grows, we start our turns earlier, making it a another step or two to the wall.|
|Leg yield facing the rails||As the horse progresses in his understanding of the training, we will ask for a leg yield along the rail, facing it so that he is less likely to run off.   The angle to the wall will be shallow enough to keep the work from causing physical or mental stress.|
|Leg yield facing into the arena||Once the horse is confidently marching forward in walk with facing the wall, we will train leg yield with his haunches to the wall.   This is much more difficult for the horse, as the arena center is like a magnet to the horse.   He will want to walk forward toward the center.   So, this movement is really a good test to see how well he understands leg yielding requests.|
|Shoulder in||The transition from leg yield to shoulder in is a subtle one.   In the leg yield, we are not worried about bend.   In fact, in leg yield, the horse is fairly straight throught the body.   However, in shoulder in we need to get a proper bend through the body, from poll to tail.   Also, the angle is quite clearly defined, whereas in leg yield, the angle can vary.   In shoulder in, the horse travels on 3 tracks.   This means that as you approach a mirror in shoulder in, you should see "3 legs" of your horse.   2 legs means you are straight.   4 legs means you have too much angle.   Shoulder-fore is a slight shoulder in often used to help balance a horse in preparation for other movements.|
|Haunches in   (Travers)||This is the first lateral movement where the horse actually looks in the direction of travel.   He moves his hind end off the track of travel of the front legs and bends through the ribs.|
|Haunches out   (Renvers)||This is the same as travers, but the haunches are pointing towards the wall of the arena.   Like the leg yield facing into the arena, this can be a challenging movement for horses still new to lateral work.|
|Half pass||When the travers is well confirmed, it is time to progress to the half pass.   This movement is often described as travers on the diagonal, and in the walk, that's good enough.   Again, the horse should be looking directly at where you are going.|
|Turn on the haunches & Pirouettes||The aids for turn on the haunches and pirouettes are simple enough, but require a high level of understanding and response from our horses.   So, to avoid messing up what will later become a fabulously fun movement, many trainers will hold off on the turn on the haunches until the aids for the other lateral movements are well understood.|
|Walk first...   Then trot !   All lateral work is trained in the walk.   This gives the horse (and the novice rider) a chance to work things through without speed.   Also, by going in walk, we give the horse a chance to build up muscles without over taxing them.   Each of these movements can successfully be done in walk and then later in trot.   Half pass and pirouettes are also done in canter.|
|Don't lean out !   When riding lateral movements, it is critical that the rider never sit to the outside of the movement.   Yet, this is one of the most common faults seen both in training and in competition.   For example, when riding down the quarterline and leg yielding to the wall, leaning towards the wall is not going to help the horse at all.   In fact, it will unbalance him, making the movement more difficult.   Always sit straight or slightly to the inside.   Never lean or sit to the outside.|
|Be successful every time !   If the lateral work you are asking for is not happening, go back to an easier lateral exercise, or get out of the saddle and return to the ground work.   Aim for one step of success, even if it's via an older lesson.|
Once your lateral work is coming along nicely, there are lots of new things to try with your horse.   Think outside of the box and see what fun you can invent.
|Side pass||Moving 100% sideways is called for in many Western Riding competition classes.   It is also useful for when trying to open and close gates from the back of your horse.   To train side pass, we use squared off jump poles that don't roll easily.   We teach the horse to stop over the pole and stand.   When he's comfortable with that, we ask him to stop over one end, then step sideways just one step, enough to not have the pole under him.   As he gets confident in this, we stop with more of the pole under us, adding more steps to move sideways.   Eventually, we get to the point where we can do the full side pass movement, starting next to the jump pole, side passing over the whole length of the pole, and coming out the other end.|
|Leg yielding into a jump||Set up 2 small cross jumps, side by side with an 8 foot gap in between them.   Riding towards the gap at the trot, decide which jump to take and leg yield smoothly towards it.   Give your horse a lot of room for this exercise, allowing the leg yield to be shallow while also giving him room to be straight for a least the last 20 feet before the jump.   And, to keep him thinking and waiting, you can sometimes trot through the gap as well.|