Sitting trot
I started like this (on a fairly understanding pony) and out of sight of other more 'proper' riders.
Take feet out of stirrups and let your legs hang down long, keep your feet reasonably flat and relax on your seat bones. Sit up straight.
Walk pony and let your legs swing very, very slightly in time with the walk (like you were walking too) you will feel your seat bones move in time with the pony.
Ask for a trot and try to maintain the same slight movement. Don't swing your legs violently, try and keep them long and relaxed. I feel my hips move, right, left and backwards and forward and my seat bones rock on the saddle. It feels like jogging on your bum instead of your feet. (Try 'bum walking' across the floor to get the feeling of the movement!)
It is important to keep the pony in a collected trot, no more than a jog really.
Eventually you can refine this until you feet are back in the stirrups and you can absorb the movement through your hip movement and don't move your legs at all. I know this is probably complete rot to any knowledgeable person but hey, works for me!
As a sad old moo with a bad back
who takes lessons in a class with lithe, young things, sitting trot (and rising trot) without stirrups are my one chance to shine whilst they bounce and slip all over the place
- one lad who rides in front of me even tries to sneak his outside foot back into the stirrup where the RI can't see and the girl behind is always being told off for holding the saddle! When we do sitting trot with stirrups they all bounce about because they appear to ride too short which throws them out of the saddle, or they frantically grip with their knees, lean forward and stiffen up.
Oh, a Heather Moffat style seat saver makes life more comfotable too!