Once you have perfected the walk in balance and this means that you can easily change your horse from a collected walk to a free walk and back again with no additional aids (other than controlling your core) it is time to move into the trot work. Begin with the walk in balance exercise (follow the link listed below) to prepare both you and your horse. Once the horse collects the walk give the aid to trot a bump or series of bumps with your inner calf muscle if you get no reaction to this give a quick lift of your heels and an instant release still no reaction you must follow through with the whip.
Once your horse is trotting in a steady rhythm, keep your feet in the stirrups and lift both of your legs up and off of the horse without changing your seat or your upper body position I call this riding with frog legs and it involves very strong core muscles. You do not need to lift them very high just enough to clear any pressure you may have on your saddle and stirrups. To aid with your security please feel free to grab the front of your saddle but please do not pull on your horses mouth to maintain your mounted position.
Your horse should not change her rhythm when you lift your legs if she does you must reestablish the trot and try again. Practice this as you can manage it if only for a second at the start it will still redistribute your weight and you will begin to develop an independent seat a must for balanced riding. Keep at it until you can maintain the same trot with which you began while keeping your legs off of the horse for as long as necessary to establish that steady rhythmic trot the horse is now in self-carriage. The more the horse carries herself the more balanced she is and the easier it will be to maintain your own centered and balanced position.
The canter work advances in the same manner as both the walk and the trot make sure you are proficient at each gait before proceeding to the next. Once you have established the independent seat at trot the canter is much easier.
In all three gaits work your core, think of how this effects your seat, then your legs, arms, feet and hands as well as your neck and head. Your legs should simply hang from the hips, your knees will fall closer to the saddle as the thigh muscles stop gripping and you relax down into long legs and soft ankles with very little pressure in your stirrups. Your arms will hang softly from the shoulders (your forearms should be carried by your own body and not on the horses mouth or neck this too comes from a strong core). Your neck is lined up with the rest of your spine and your head rests upon this soft and strong neck. As long as your core muscles are engaged the rest of your body is free to address the horse this is true balance.
As you progress through all of your training I trust you will come to understand that as a horse/rider entity you move up the ladder together but perhaps not equally. Sometimes the horse progresses faster thusly allowing the rider to catch up with greater ease. Other times the rider surpasses the progress of the horse which then allows the human half of the equation to assist the horse in his/her improvement. This is normal as we all, people and horses, learn in varying and different ways. The critical point to remember is to just keep at the correct aids, without inventing new aids if you and/or your horse are struggling in time and with a little patience and lots of practice both of you will be riding in balance and harmony. Then the next time someone watches you ride they will wonder how you mange it all without ever moving a muscle.