There is no one right way to learn a pose, or to get into a pose once you've learned it. For example, LoY instructs most of the classic level 1 lateral-angle standing poses (such as Triangle and Side Angle) from the starting point of Mountain pose. But at least one reputable lineage of practice often builds their standing poses from starting in a basic runner's lunge position. Is one better than the other? No, not unless one happens to be better than the other for you. And all sorts of contingencies are going to influence that; at the very least, which parts of your body are stiffer and/or stronger than some other parts. The point is simply that there is more than one good way to learn any given pose.
Lying on the floor happens to be one very good way to learn (or refine) poses. Nearly any pose or individual components of poses can be evaluated and clarified from a reclined position. One benefit to lying on your back is that the floor is doing a large part of the hardest work for you; that is, supporting the spinal column. Of course, without some appropriate use of toning and overall awareness, the lumbar or cervical curves could flatten. But the amount of effort required to maintain good spinal form is distinctly less when lying down than in any other position. And you have eliminated other challenging aspects such as balancing. Because you exert less effort on keeping the torso well-formed, you can distribute that energy and attention out into the limbs and their joints. In other words, a body-shape which is challenging to perform while standing or sitting or inverting may be more accessible while lying down. A few example: Reclined Hand-to-big-toe pose (Supta Padangusthasana, 244) first stage can teach you a lot about Intense Side Stretch (Parsvottanasana, 78), which is a basic standing pose, as well as inversions such as One-legged Headstand or Shoulderstand (Ekapada Sirsasana, 199 or Ekapada Sarvangasana, 223). The second stage of Supta P. is a great resource for understanding something as elementary as Triangle pose (Trikonasana, 63) as well as something more advanced such as Side Plank pose (Vasisthasana, 311). And Happy Baby (Ananda Balasana, not in LoY) is fantastic preparatory work for Crow pose (Bakasana, 315) and other arm-balances.
Of course they are not perfect replications. And there are limitations and exceptions to floor work. Anything that requires arm or leg extension into the back plane will be difficult or even impossible. Supta P., for instance, while it does give you an opportunity to improve the leg and hip mobility required for Parsvottanasana, it can't do much to help with that pose's traditional Reversed Prayer hands. And Reclined Hero (Supta Virasana, 123) is a wonderful way to prepare for a back bending sequence IF you can get into the pose. If you cannot comfortably get into Supta Virasana, then getting to the floor may be your peak rather than your prep.
What I hope to highlight here is that much can be gained from finding relationships between poses, and one such relationship which tends to be particularly helpful is recreating a pose or part of a pose with the support of the floor. Don't reinvent yoga every time you introduce yourself to a new pose. The body is complicated and intricate, but the ways in which it moves is in fact finite. Many of the poses are simply variations of each other with various relationships to gravity. So look for relationships and similarities, and use poses to learn other poses.
The following is the sequence we practiced in class on 12/7. We used reclining leg and hip poses as preparation for Shoulderstand variations. You can modify, decrease, or embellish this sequence in any way that works for you. You may want to add some rounds of Sun Salutation to the beginning, some poses to open your shoulders and upper-back, or, rather than spending the second half of the practice in Shoulderstand, you could use the reclined work as preparation for the standing sequence.
Opening meditation and any warm-up you desire
(Hold the following 5 poses for 1 minute each on the right side first, and then repeat each of them on the left side.)
1. Reclined Hand-to-big-toe pose (Supta Padangusthasana) variation with hands clasped behind thigh
2. Supta Padangusthasana first stage (either holding the big toe, the foot or ankle, or a strap around the foot)
3. Supta Padangusthasana second stage (with leg extended out to the side)
4. One-legged Happy Baby (Ekapada Ananda Balasana, not in LoY)
5. Eye-of-the-needle pose (Succirandhrasana, not in LoY)
Repeat poses 1-5 a second time on each side
Upward Extended Foot pose (Urdhva Prasarita Padasana, 240-242) 3-10 times
Revolved Abdomen pose (Jathara Parivartanasana, 237-240) 2-3 times per side
Happy Baby (Ananda Balasana)
Supported Shoulderstand first variation (Salamba Sarvangasana, 205-213) for at least 5 minutes
Plow pose (Halasana, 216) for 1-5 minutes (if your toes do not comfortably rest on the floor overhead, you should continue practicing first variation Shoulderstand and Plow before moving on)
(each pose in the Shoulderstand cycle can be held for 10-30 seconds)
Ear-pressing pose (Karnapidasana, 220)
Reclined Wide-angle pose (Supta Konasana, 221)
Side Plow pose (Parsva Halasana, 222)
One-legged Shoulderstand (Ekapada Sarvangasana, 223)
Side One-legged Shoulderstand (Parsvaikapada Sarvangasana, 225)
Finish your practice with any seated or reclined forward folds or twists that leave you feeling balanced, whole, and ready for several minutes of relaxation
Corpse pose (Savasana, 422) for 5-20 minutes
As you move from pose to pose, think carefully about what you're doing while you're doing it for the sake of the present moment, and at the same time consider how what you're doing now may be related to upcoming actions. Where are the repetitions and similarities? Which poses most clearly inform others? Which poses most effectively teach or prepare you for others? Be receptive and curious. And questions and comments are always welcome.