This is how you perform the half butterfly yogasana:
Sit on your mat.
Fold the right leg and put the right foot on the left thigh.
Keep your left hand on the bent right foot over your thigh, and the right hand on the joint of the right knee.
Now, move the bent leg up and down gradually with your hand placed on the knee joint. This should allow your leg muscles to relax as much as possible. Try to touch the bent knee to the ground while moving it up and down.
Repeat the same steps with the other leg after reversing your position.
Repeat the same process with the left knee. Practicing this for some weeks would make your joints and bones flexible enough to touch the floor without effort.
Some precautions or modifications in the practice of Half Butterfly Yogasana based on your health condition:
The type of bends and flexes required in this asana can aggravate your sciatica. Patients of sciatica should keep their hips elevated while performing this exercise by placing a cushion for sitting. It would be advisable to not do this exercise at all if you cannot bring your knees below the hips. Make absolutely sure that the hips do not rotate backwards while sitting to avoid complications, as they need to rotate forward.
People with lower back disorder should guard against any type of flex in the spine. Make sure that the back is as straight as possible while you move the knees up and down. You might consider reclining comfortably to do the exercise.
If you have a problem of pain in your knees, you can get round the discomfort by tightening your grip of the knee joint and tightening the top of the thigh. You can also bring the legs closer together to avoid pain.
If you have complication of pain during the bending of knee, put some sort of support under the respective thigh. You can also move that foot away from the groin to avoid pain.
If your hamstrings do not let you perform the exercise, keep a support under the bent straight knee. It could be a blanket or book.