Lol riding a horse like that and doing a sitting trot is far, far removed from riding a sitting trot on your garden variety hunter.
That horse, as much as the trot looks huge and terribly difficult to ride, actually has that nice supple back that with the right amount of core strength sucks you right into the tack. On my horse I actually find his extensions easier to ride than his collected trot because there is greater impulsion and his back becomes more supple with that.
Anyways, I like Lydia's explanation quite a bit. I actually find the most difficult thing in the sitting trot is dealing with the stirrups. Start without stirrups (but keep your toes up) and get your pelvis going in the right way. Then, start with longish stirrups and try to keep your knees and ankles relaxed that they can absorb the motion, and keep your legs in a barrel shape that they may also accordion outwards in the downward part of the stride. Slowly shorten the stirrups to your normal length and then you should be set.
The key is the core in any sitting trot, but keeping your pelvis soft and able to follow the horse.