Excellent advice, and Tinyliny beat me to the punch regarding NOT tightening the buttocks. Tightened buttocks "bounce" in the saddle and prevent (as Tinyliny said) the seatbones from contacting the saddle correctly. Her description of the core muscles was right on, too.
I also like anebel's description of feeling as if your leg from seatbone to ankle is 1 mm from the horse -- as if you're "hovering" lightly on the horse. This is not something to "work" on physically, it's more of a mental thing. (Am I right, anebel? Correct me if I'm misinterpreting your intentions.)
Do NOT lengthen your stirrups! Too many riders, trying to "get" the dressage seat, misinterpret the idea of the long dressage leg. Often it's better to SHORTEN your stirrups a hole or two because a too-long stirrup actually creates more tension and imbalance in a rider. I struggled mightily for years with an instructor who insisted I had to learn to ride with a longer leg, and that meant a longer stirrup. I rode in a dreadful crotch seat and all my photos from that period of time show me pitched forward with ineffective legs.
Dittos the suggestion to get lunge lessons, preferably without stirrups. It really is the best way to improve the seat. If that's not possible, ride w/o stirrups, if only at the walk at first. Then shorten your stirrup leathers a hole, allow your buttocks to relax, and don't use your thighs. Tightened thighs are much like the tensed buttocks -- in fact, it's pretty hard to have one set of those muscles relaxed and the other set tense. Horses, especially sensitive ones, find tensed seat muscles either irritating or constricting. Some will "run away" from a tense seat & thighs, others react by shutting down and slowing forward movement, as if the tight seat is a straight jacket.
It sounds as if you need first and foremost to learn to follow the horse's movement. Think of it this way; you and your horse are dancing the Tango or some other slinky Latin dance. Think of the way good dancers follow and mirror each other's movements and how their bodies move together. Imagine that your hips move with your horse's hips. As his right hind leg reaches forward, your right hip moves in concert with it. Feel how his belly sways back and forth, right and left as he steps. Feel it with your seat and roll with the horse's movement.