While doing exercises in the saddle pay attention to your horse's reactions. If you are not sure what your horse may do then have someone walk him or keep you on the lunge line during the exercises.

First, work on the exercise off the horse. Sit on a hard chair. Legs slightly apart and keep your back straight. Do not lean back and do not round your back. Make sure your pelvis is in a neutral position. Imagine that you want to pinch your chair seat with your seatbones. Muscles that you sit on will engage and you will get a feeling of lift from underneath. Hold for a few seconds, then relax. You may find that, in the beginning, engaging muscles under your seatbones is very hard to accomplish. The engagement is weak and indistinguishable. Do not give up. Work on it any time you have a chance and you will get better.
After a few times in the chair try it on a horse. It will be hard to focus on the exercise and to ride at the same time. Work on it during warm-up or cool-down walk, or during walk brakes on the long rein. Make sure your thighs are rotated inwards and your pelvis is in a neutral position. Try to engage muscles under the seatbone in the same way you did in the chair. At first, you will have to focus very hard, but when you get better your muscles will stay engaged without your constant attention.
Variant: To better understand why you need to have these muscles engaged, switch between tightening them and relaxing completely. Observe, how wobble and unstable you become when everything is relaxed. On the other hand, when muscles under the seatbones are working they create a feeling of stability and connection to the saddle. They should not be tight as a rock. However, complete relaxation will create instability.

Do this exercise during the walk on the long rein. Make sure your thighs are rotated inwards and your pelvis is in a neutral position. Try to lift your legs directly sideways and up without losing rotation. Do not rotate your thighs outwards. Make sure, nothing else is moving. Do not arch your back, or tuck in your pelvis. Believe me, this is very hard. For the first time, you may not be able to lift them at all. If this happens, simply engage your muscles without actual movement. Once you get the correct motion, lift and relax the legs several times while your horse is walking.
Variant: Try to combine this exercise with the previous one. Engage muscles under the seatbones and lift your legs at the same time.

Do this exercise during the walk on the long rein. Drop your stirrups. Make sure your thighs are rotated inwards and your pelvis is in a neutral position. Slide a little bit to the right. Now, using your left thigh bring yourself back into the center. Now slide to the left and use your right thigh to bring you back. Pay attention not to do any extra movements. If your thighs are weak you will start wreathing in the saddle trying to bring yourself back. If that is the case, slide to one side just a little bit. Observe, which direction is easier to slide to and which direction it is easier to come back from. Repeat several times on each side.

Do this exercise during the walk on the long rein. Make sure your thighs are rotated inwards and your pelvis is in a neutral position. Rotate your whole body, including your hips, to the right . You will get a feeling of pushing your right hip backwards and your left hip forward, use your thighs to help you with the rotation. Come back to face forward and then rotate to the left. Observe the moment when your hips can no longer rotate and your upper body still can: how much more can you rotate your upper body after your hips stop? You will see there is a difference between the left and right sides of your body. You may realize that it is easier to rotate the hips in one direction, but the upper body doesn't go very far after the hips stop moving. When you rotate in the other direction, it is hard to rotate the hips, but the upper body turns easily. Work twice as long on the parts which are reluctant to move. Repeat several times.