In the marichyasana series of binding yoga poses you generally bind the marichyasana leg either from the inside (and bend forwards) or from the outside (while twisting.) These binding yoga poses can be a little bit challenging because you are binding both the thigh and the shin.
In Marichyasana A, the non-marichyasana leg is straight and the bind is accompanied with a forward bend.
The further forward you can bend in this yoga bind, the easier it is to bind since bending forward brings the shoulder of the binding arm past the front of the shin.
As in the Easy Marichyasana B, you can let your hips lift off of the floor in order to make it easier to bind.
Note, you don't have to lift your hips in order to bind in marichyasana A. If you are flexible enough, leave your hips on the floor and bend forwards. You can use one hand to help you bend forwards while you reach the other hand forwards inside the marichyasana leg.
One point that is important when doing Marichyasana A is foot set-up. When first doing this pose (or variations of it) students tend to position their bent knee foot close to the inner thigh of the straight leg. I prefer to position the foot wider so that viewed from the front the outer edge of the foot is inline with or to the outside of the outer edge of the hip.
If you wanted to move from this seated position into a one legged pistol squat then having the foot close to the center line of the body (close to the inner thigh of the other leg) would be a better position. Your foundation is then closer to being under your center of gravity. However, when doing Marichyasana a, whether just bending forwards, or bending forwards and binding, the wider foot position feels more stable.
See the link at the bottom of the page for why allowing the marichyasana leg hip to lift is good for the sacroiliac joint.
To make it easier to lift your hips, place your straight-leg hand on the floor behind you and to the side. Push yourself away from your hand so that your hips lift and your torso moves forwards.
You could hold this position for a few breaths. Try pressing down through your marichyasana foot as well as your hand. Use the hand that is on the floor to push your ribcage towards your bent knee as well as forwards.
While holding this position (with either hips lifted or on the floor) you can reach the bent knee arm forwards. Work at making both it and your spine feel long. For maximum length in the arm try to protract the shoulder blade.
Hold for a few breaths and when you are ready, reach the arm to the side in front of the marichyasana shin. Here again hold for a few breaths.
Try to keep the feeling of length in the arm. Then, internally rotate the arm so that the point of your elbow points forwards as much as possible so that when you bend your elbow your forearm reaches behind, and up your back.
This action, rolling the arm inwards, may cause some muscle spasms the first few times you do it. Part of the way around that may be to work at stabilizing the shoulder blade while you do it so that your shoulder rotators have a stable base from which to work.
Dance of Shiva provides one way of practicing scapular control while the arms are rotating.
Another way to practice stabilizing the shoulder blades while internally rotating the upper arm is with the Penguin Shoulder Stretch
Try to hook the leg with this arm so that you can lift the other hand.
So that you can lift your other hand you may find it helps to push down through the heel of the straight leg. You may find it helps to turn away from your marichyasana leg as your reach the straight leg arm behind yourself. Grab that wrist with your other hand (or try to).
In Ashtanga Yoga, in all of the marichyasana positions the binding arm (the arm wrapping in front of the leg) is the grabbing hand. That being said, you may find it interesting to switch grips and notice the changes that this creates. You may find it easier to grab the other way. You can then use this "reversed" grip to pull the arms deeper and then from there switch back to the "proper" grip.
Once you have bound, or clasped your fingers (or grabbed onto a towel or strap with both hands), hold with your torso turned away from the marichyasana leg for a few breaths. Then try to turn forwards. From here, push your arm back against your shin to help your forward bend.
As you bend forwards in Marichyasana A you may like to reach your hands back as if to straighten the arms. This may give you more leverage to bend forwards, using the arm to push back against the leg. In addition you can shift weight onto your marichyasana foot and press forwards with the shin.
If you are no where near binding, you can try hugging holding on to your knee while sitting upright. You could also place a hand on the floor behind you to keep yourself upright. Rather than trying to bend forwards you could work at lengthening in this position. Make your spine long (even if you have to lean back) and reach one arm forwards and make it feel long also.
To release from Marichyasana A, assuming you are bound, try releasing your grip smoothly. You can then switch sides. If you are doing it in the context of an Ashtanga practice you might choose to lift up from Marichyasana A and do a series of transition poses including Eka Pada Bakasana before doing the other side.
As a yoga teacher, I'm constantly exploring new exercises, new ways of doing yoga poses.
There is no single "right way" of doing a yoga pose. Instead, there are options. And the better you are at "feeling" your body, the better you can get at choosing the right option for your body as it is now.
For any technique, the point of practice is to learn feel it and to control it, so that it can be used without thinking about how to use it.
And that is more or less the approach taken in all of my ebooks and videos. They help you to feel your body and control it so that you can work towards using it effectively in anything that you do.