Dawn and I have been doing some lateral work at both the walk and trot - we've started with leg yield, just trying to get a good step or two at a time with the least aids possible. Doing this work has made me think about how important it is to ride the hind end of the horse rather than the front end. There's so much horse in front of us when we're in the saddle - the head, neck and shoulders - and that's what we see (particularly if we're looking at our horse's head rather than at where we're going!), and we're holding the reins, so it's natural to ride the front end of the horse. I also think many of us are taught to ride using way too much hand (I know I was), and to pay too much attention to the position of the head and neck and not enough attention to the "feel" of the horse's movement and the softness or lack thereof. There's also a (in my opinion bad) practice in certain disciplines of driving the horse from behind into your hands (I was also taught to do this) - that's a great way to get a horse that's braced from nose to tail. Depending on your discipline, you may ride with contact or without it, but the role of the hands should be to give direction and to allow the motion, and to set boundaries (which need some elasticity) to the horse's head and neck position - but not to pull or force the horse's head into a particular position, or to act like a fifth leg and hold a leaning horse up.
My objective with my horses is self-carriage, where the horse's core is engaged and the top line is relaxed, with the result that the horse can move effectively, with softness. This requires that I ride the hind legs in terms of their activity and engagement. I try very hard not to push or drive with my legs or seat - I want my aids to be soft, not heavy - if I need to get a horse moving forward that isn't responding to a soft leg aid I add a secondary cue like a crop on my leg or the saddle (that's what I've been doing with Pie and to get Drift past his balking) - if I up the aid, I'm only training the horse to respond to that stronger aid rather than the soft aid I want the horse to respond to. Also, pushing or driving with the legs or seat tends to create a brace in the rider's body that the horse will then brace against and also restricts the horse's motion. I'm a big believer, with a horse that understands basic softening, in doing lots and lots and lots of transitions and also figures - circles, spiral in/out, serpentines, etc. - to help the horse learn to carry itself without my pushing with my legs or seat or pulling with my hands.
Helping the horse move more effectively also requires that I feel where the hind legs are and what they are doing - this allows me to "ride" the individual hind legs to time my cues when a particular hind leg that I want to do something is in the air so that the horse can more easily respond in a correct manner - this is useful for all sorts of things: canter departures (if you time your cue correctly when the hind leg needed to initiate the canter is in the air, the horse will take the correct lead, immediately), lateral work where a hind leg should step under (rather than the front end moving over and dragging the hind end along) and even turns or corners where I want the inside hind leg to step under, and halts - riding the hind legs is a great way to get square halts without the horse falling on the forehand.
So, when I'm asking Dawn to leg yield, at the walk I was focussing on the (outside) hind leg that I wanted to step under and lift her to the inside. At the walk, the horse's barrel swings from side to side - when the barrel is swinging away from your leg (toward the middle of the horse), the barrel is getting out of the way of a hind leg that is stepping forward. So to time my leg aid to ask that hind leg to move under, all I had to do was to follow the barrel as it moved away from my leg toward the middle of the horse, applying my leg aid, and voila! the hind leg would step under and carry her sideways. I also had to be sure to "allow" her motion by creating an opening for her to move into on the other side by not restricting with my leg or hand - if I think of my moving my own legs in "human leg yield" that feel is communicated to her. The same idea applies at the trot and canter, although learning where the hind legs are as the horse is moving takes some practice - having a helper on the ground practice with you as you say "right" (hind) or "left" (hind) as a hind leg leaves the ground can be very helpful.
It's fun riding the hind legs - all that wonderful power from the hindquarters is at your disposal and you can send it wherever you want - sure beats riding the head, at least in my book, in terms of how it feels and the results. (I've added this post to the "Working Towards Softness" sidebar.)