When doing yoga for flexibility, know the general direction you are trying to move one part of the body with respect to another so that you can then focus on the muscles that are inhibiting this movement or the muscles that can aid it.
To deepen a stretch you can work at relaxing the muscles you are stretching. Or you can focus on keeping them active as if resisting the stretch.
Another way to move deeper into a stretch is to use muscles that oppose the muscles being stretched. So to stretching the hamstrings activate the hip flexors, the muscles that work on the front of the hip. When using this technique it helps to understand reciprocal inhibition. It's more than just tensing an opposing muscle.
The following yoga stretches (for improving flexibility) are grouped according by body part.
Wall Stretches, Arm and Shoulder Stretches, Back Stretches, Hip Flexor (and Psoas) stretches, Quad stretches, Hip Extensor stretches, Hamstring stretches, Glute and Piriformis Stretches and Adductor stretches.
If your flexibility is limited you may find it useful to use a wall to make increasing flexibility easier.
Using a wall for these yoga stretches, you may find it easier to use muscle power or gravity (or both) to take you deeper into each stretch.
The muscle assisted shoulder stretches are if you want to work while stretching. The gravity assisted arm stretches are for a more relaxed stretching experience. Both types can be used to help improve shoulder flexibility
Yoga shoulder stretches includes traditional yoga shoulder stretching positions like reverse prayer, eagle pose and the shoulder stretch used in prasarita padottanasana C. Hip and Shoulder Stretches are poses which stretch the hips and shoulders at the same time.
Lower back stretches include a variety of standing and seated yoga exercises for increasing the flexibility and control of the lower back muscles and hip muscles. If you have low back pain, you may actually be suffering from weak or imbalanced or ill functioning hip muscles. So if you low back pain is chronic look at exercises to strengthen and stabilize your hips. Standing yoga poses are useful in this regard and balancing on one foot more so.
To focus on your upper back you can try these upper back exercises. You may find some of the shoulder stretches (below) also helpful for tight upper backs.
When you stretch your back you are actually stretching a part of your spine. Here's a comprehensive list of spine stretches.
Hip flexor stretches work on the front of the hip. These may be useful as warm ups or compliments for quadriceps stretches.
Front to back splits is both a hip flexor stretch and a hamstring stretch though with the torso upright the focus is more on stretching the hip flexors (and psoas) of the rear most leg.
The psoas is a hip flexor (and a lumbar stabilizer). One way to stretch the psoas is with a Reclining Psoas Stretch. Part of what makes this stretch interesting is that it is based on the understanding that the psoas connects to the 12th set of ribs. You can also stretch the psoas with a Standing Psoas Stretch as well as these Standing psoas stretch variations. Other stretches include some Active Psoas Stretches.
One method for stretching the psoas includes learning to add "inner tension" to the lumbar spine. This is covered in psoas stretches. Another technique is to keep the abs engaged, in particular the obliques. This is covered in psoas stretches-1.
Yoga for flexibility exercises that stretch the quadriceps all involve "closing" the back of the knee joint.
Easier quad stretches are those where the hip joint is bent forwards (flexed hip stretches) while more challenging quadriceps stretches are those where the hip is bent backwards (extended hip stretches) such as in reclining hero pose.
If you have difficulty stretching your hamstrings you may find it helpful to stretch the back of the hips by doing bent knee hip extensor stretches first.
Glute stretches like low lunge, modified marichyasana e and Happy Baby Hip Stretch) can be used to increase flexibility at the back of the hip when the knee is bent. This can mean muscles like the adductor magnus long head are affected (since it can extend the hip), as well as some fibers of the gluteus maximus.
If you have tight hamstrings you may find it easier to start with these stretches for tight hamstrings. As hamstring flexiblity improves you may find seated hamstring stretches easier, particularly when you learn how to add weight to your stretch.
For more on how the hamstrings and glutes work together in different yoga poses you may find the hamstring anatomy article useful.
You may be surprised to find that the calves affect the hamstrings and vice versa.
What is really interesting is how these two sets of muscles affect each other in straight leg positions. Often times the stretch you feel in a forward bend (or the discomfort) isn't so much the hamstrings but the calves.
The calf stretches article includes both passive calf stretches (like the ones shown above, and active calf stretches. Be prepared for some discomfort!
In general these glute and piriformis stretches include an external rotation of the thigh relative to the pelvis with a forward bend.
One of my favorite glute stretches is pigeon pose glute stretch.
While it may not be possible to stretch the actual Iliotibial band (also called the fascae latae), you can stretch some of the muscles that work on it (fibers of the gluteus maximus, tensor fascae latae and vastus lateralis) with shoelace pose.
These yoga for flexibility poses mainly stretch the inner thighs but also include poses where one or both legs are internally rotated.
Inner thigh stretches work on the adductors, the muscles that pull the legs inwards. This includes the adductors brevis, longus and magnus, pectineus, gracilis and perhaps also the psoas and iliacus.
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.