This is a really hard topic to explain, as most people use their seat differently, and it's something that is really difficult to describe in words. I'll tell you how I use my seat, and see how I go :] I ride a lot of different disciplines, but mainly speed events like mounted games and Campdrafting, as well as showing in ASH classes, which involves fast stops, spins, haunch turns, rollbacks and backing up. So the way I ride may not be practical for you at all!
I have three 'seats', I suppose you could say. A neutral seat, a blocking seat, and an open seat.
Neutral Seat - What I use when travelling, and not asking for anything, i.e. we are at my desired speed/impulsion and I just want it maintained. I try to sit quietly, absorb the shock of movement up through my core, and let my legs kind of 'hang' down and around my horse. I only move/change from this seat when I need to ask something, wether it be a lengthen, shorten, stop, turn, etc.
Blocking Seat – This is the seat/action I use when I need to shorten, transition down, make an abrupt turn, or a dead stop. What I am asking for determines the strength of the ‘block’. This one is the hardest to explain… It’s almost like ‘closing’ your pelvis. I kind of ‘contract’ my position… I contract my core muscles, and my thighs contract around my saddle while my heel pulls down to give me security in whatever I’m about to do. I also kind of rotate my pelvis forward which in turn puts more weight in my seat and puts a bit of a ‘hunch’ in my back, not enough that you can see, but enough that I become heavier on the horses back and it also gives me a bit more security in a fast turn or fast stop. So basically my whole body contracts and ‘blocks’ forward movement. However, I only ever do this for one step, except in the case of a back-up. I always pre-empt the block with a half halt so my horse is ready. I use this softly for a shorten, stronger for a downward transition and a back up, and stronger still for an abrupt stop. When I use this for a turn, I use the block to arrest forward motion for a second, and then cue the turn. For a back up, I start at a halt, and move into my blocking seat rhythmically, kind of like you would bump your horse with your legs. To end the back-up, I return to a neutral seat. If a horse doesn’t understand the block, I always start at a walk, and ask for a halt with the seat, and follow up with the rein. Eventually they learn to follow the seat.
Open Seat – What I use when asking for lengthen, upward transitions, etc. It is kind of the opposite of the blocking seat. I ‘open up’ my pelvis, which allows my legs to stretch longer, and straighten my core without becoming rigid, and open up my shoulders. It makes me lighter in the saddle, as well as presenting a lot of forward energy to the horse. I use this lightly for lengthen, a bit stronger for an upward transition, and stringer again for transitions like walk/canter, halt/canter, and then to an extreme when I’m gaming/cow chasing for an abrupt halt/gallop. I also use this to power out of sharp turn such as rollbacks and haunch turns.
A sharp turn is the most complicated manoeuvre in regards to seat, for me anyway, as I cycle through all three within about 3-4 seconds. A blocking seat (gently) to rock him back on his haunches, a neutral seat with turning aids to make the turn, and an aggressive open seat to ask him to power out of the turn.
A really good exercise I use when my horse isn’t listening is to canter a circle in neutral seat, use a blocking seat to halt, rollback to the outside of the circle and use an open seat to canter depart straight out of the rollback on the other lead. I do this a few times either way and my horse starts to listen and really give me snappy stops, turns and departs.
My rains are only used to cue turns, and also to ask for vertical flexion. Sometimes horses who are directed purely by the seat get into the habit of butting the nose out when asked to halt/back up with a blocking seat, as happened to me when I was riding a lot bridleless. So the reins are used to ask or reinforce vertical flexion when stopping or backing up.
Anyway, that may not have made any sense, but I hope I helped!