One thing to consider when doing twisting poses (spinal twists) is to anchor the base of your spine. That can mean stabilizing your legs if standing, or stabilizing your hips while sitting. That being said, you could also work at stabilizing your legs (as well as your hips) while doing seated twists.
If you are twisting while supine or prone, generally your turn your pelvis relative to your ribcage. In this case, you could work at stabilizing your upper body. However, to make your lumbar spine more comfortable you might choose to stabilize your hips and lower back, especially if using the weight of your legs to drive the twist.
While you can use your arms to help drive a twist, particularly while seated, I'd suggest learning to activate your spinal muscles and using them to generate a spinal twist. As mentioned, muscle activation tends to give you sensation. If you activate your spinal muscles while twisting, they'll not only help you twist your spine, they'll also help you to feel it.
Twisting poses can be used to twist the spine and can be used to stretch the hips by turning the pelvis. When doing active twists you can use the obliques and intercostals as well as the gluteus maximus to drive the twisting action. With passive twists, you can use gravity to help drive the twist. That being said, you may find your twists are a lot more comfortable if you resist the stretch slightly. So rather than just "flopping" into a passive twist, use the muscles you are stretching to resist the stretch, just enough to give you some feeling and some control over the twist.
When doing assisted stretches, you'll be using your arms (and/or legs) to help drive the twist. Here too, you may find the twist a lot more comfortable if you resist the stretch with the muscles that you are stretching.
Going back to active twists, in active twists you can use opposing muscles against each other to control your spine as you twist it. As one set of muscles shortens, the opposing muscles lengthen. This allows you not only to control the twist, it also allows you to feel it since muscles on both sides of the twist are active, and working against each other.
I mentioned above that some of the main muscles you can use when twisting are the obliques and intercostals. Other muscles also include the spinal erectors and the smaller paraspinalis muscles and even the psoas.
To learn how to feel your spinal erectors, and activate them, check out the spinal back bending exercises article.
For more on the spine in general, and the ribcage, check out the Intentional muscle control courses 8 and 9 below.
As mentioned above, in active twists, the idea is to use muscles of the spine to drive the twist. This can include the intercostals and obliques, but it can also include the spinal erectors.
The first goal in an active twist can be to turn your ribcage relative to your pelvis.
For seated twist have your hands together in prayer and keep your hands in front of your sternum. Twisting to the right focus for a few breaths on pulling the right side of your ribcage rearwards. Then focus on pulling the left side of your ribcage forwards.
Try pressing your left foot down into the floor so that your left gluteus maximus activates then try to deepen the stretch while keeping it activated.
(For alternative activations, read Seated Twist)
For a standing spinal twist, you could work at keeping your pelvis square to the front. Then use pull one side of your ribcage rearwards relative to your pelvis and the other side forwards.
Another option is to allow your pelvis and ribcage to turn to the same side. Then stabilize your hips. Standing spinal twist explains how and why you should stabilize your hips along with how to deepen the twist.
You could also practice twisting while walking. Read walking with a twist to find out how.
You can try the same thing in parivrtta trikonasana (revolved triangle). Start with your hand on the floor. Turning to the right you can activate your left gluteus maximus to help deepen your twist. Use your left arm against the floor to help. Then relax the arm and lift the hand. Keep your butt active and try to use your abs to deepen the twist.
Moving to the floor, in prone twist, you have the option of trying to relax into the twist, using gravity to help turn your ribcage. To ease the possibility of neck strain start with your head turned in the same direction as your legs. Use your arms to help turn your ribcage. Or use your abs and intercostals. Or use both sets of muscles together. To resist the stretch press your bottom knee into the floor, as if trying to turn your pelvis in the opposite direction to your ribcage.
Turning to the right try to lift the right side of your ribcage. Press the left side of your ribcage down. Once you've turned your ribcage far enough, then also turn your head in the direction of twist, so long as your neck stays comfortable that is.
While in most twisting poses the emphasis is on turning the ribcage relative to the pelvis, in this shoulder stretching and twisting pose called lapasana you can focus on turning your pelvis relative to your ribcage. With the right arm being stretched, focus on turning the pelvis to the left.
With legs crossed on in a semi-kneeling position (above right) you can use your arms to help twist your spine. Turning to the right use your left hand to help pull the left side of your ribcage forwards. Use the right hand (on the floor behind you) to pull the right side of your ribcage rearwards.
If using the semi-kneeling position you can twist towards the kneeling leg or the non-kneeling leg. In either case you can use your arms to help drive the twist.
With the hands in prayer you can rest one elbow on the floor, on in the case of twisting side angle, against the thigh. Press down with the bottom elbow first so that you use the shoulder of the bottom arm to help the twist. Then by pressing the top hand down against the bottom hand you can activate the shoulder of the upper arm also.
You can use this same action in the pigeon pose glute stretch. With the front leg hip on the floor try to hook your bottom elbow into the bottom of the foot. Press the elbow and foot against each other so that both limbs are working. Then put the hands together in prayer and use your top hand to help the twist also.
A twisting pose that is similiar to side angle pose but that is done while seated is ardha matsyendrasana. Twisting to the right your left arm presses against your right leg. So that the arm has something stable to work against, press your leg outwards against the arm. Then press the arm inwards against the leg to help turn your ribcage.
A further option is to reac the hand beneath the leg so that you can grab the other hand behind your back.
In this case you may find it helpful (for your shoulders) to sink the left side of your chest down while lifting the right side upwards.
The marichyasana series of yoga poses are poses where one knee is bent with the knee pointing upwards and the foot on the floor. In all of these pose you bind by wrapping the arms around the leg and grabbing a hand behind the back.
One example is an easy twisting version of marichyasana b.
I'll call this an easy twist or open twist since the twist is away from the marichyasana leg.
Read here for the full version of marichyasana B
Marichyasana a can also be turned into an open twist. Normally you bend forwards in this pose. Turn it into an open twist by turning away from the marichyasana leg. If the right leg is in the marichyasana position then twist to the left.
In Marichyasana C the non-marichyasana leg is straight and you twist towards the marichyasana leg. This then is a closed twist. Because the binding arm (the left arm in this case) tends to want to slide off of the knee, pulling down on the left ribs and left shoulder may make it easier to maintain this pose.
Marichyasana E is done with the non-marichyasana leg in hero position. Turn it into an open twist by turning away from the upright leg.
In the Bharadvajasana twist one leg is in hero and the other in lotus. Twisting to the right the right leg is in lotus and the right hand grabs the foot from behind the back. The other hand rests on the lotus leg knee or on the floor with the hand under the knee (not shown.) Pull the lotus foot forwards as if trying to pull free of the hand. At the same time pull back with the hand. Use the tension in the bound hand and leg to help pull the right side of the body rearwards. Or turn this into a shoulder stretch by trying to turn the ribcage to the left.