Yoga poses can be used as leg strengthening exercises in several different ways.
A key to making yoga leg strengthening exercises progressive is understanding leverage (or moment arms).
Seated yoga poses with one or both legs straight (and either forward or to the side) can be used to strengthen the hamstrings and glutes.
In the pictures below, I'm using hurdlers stretch to strengthen the hamstrings and glute of the straight leg.
While bent forwards towards your straight leg, start with your hands on the floor. Press the heel of the straight leg down into the floor so that the back of your leg activates.
Relax and repeat, noticing the tension along the back of your leg that occurs when you press your heel down.
So that your leg muscles have more weight to work against lift your hands. Note that this doesn't mean reach them forwards! Just lift your hands off of the floor. Then put your hands down and then relax your leg. Repeat a few times, synchronizing with your breath.
Reaching the arms forwards shifts the center of gravity of your upper body further forwards, away from your hips, increasing the moment arm or leverage.
In simple terms it means your legs have to work harder to keep your body lifted.
So that you get better at feeling and controlling your leg muscles, initially focus just on pressing your foot down and activating your leg. Once you get the feel of your muscles activating, then repeat the exercise while synchronizing with your breath. Inhale as you press down and then reach. Exhale as you put your hands down and relax.
One reason for synching your breath with these movements is so that you remember to breathe.
To strengthen the outer hips in bound angle pose, press the feet down into the floor.
Sit with feet together and knees bent outwards. Ideally have your heels close to your pelvis, but if this hurts your knees then try it with the feet further forwards.
Place your hands on the floor behind you to help keep your body upright. Press the outer edges of your feet into the floor while using your hands to keep your torso upright. You might feel as if you are trying to lift your hips. But keep them on the floor as you press down.
Again do it repeatedly and focus on slow and smooth activations and relaxations.
For this version of side plank the focus is on using the bottom leg so that you strengthen the outer thigh.
Focus on pressing the outer edge of your bottom foot into the floor. Press in such a way that the front and rear of the outer edge of the foot have even pressure. Your foot should be strong or active.
Once comfortable with this general action (practice pressing then relaxing), press down with enough force to lift your hips.
Lift just high enough that the outside of your bottom leg and the bottom side of your torso form a straight line. Adjust your hip height so that the hip feels comfortable.
One version of side plank focuses on the top leg. With your bottom knee on the floor, hips lifted, and the sole of your top foot on the floor, press the top foot down into the floor so that your inner thigh muscles activate.
With your hand on the floor you can then lift the bottom knee.
If you press down your top foot strongly enough it should take little extra effort to lift your knee.
Adjust the height of your pelvis so that your hip joint feels comfortable.
This pose can be used as a warm up for the leg strengthening exercise that follows (half split).
In a pose like half split you can strengthen your inner thigh by pressing the foot of the straight knee strongly into the floor.
Practice first in an upright position with your bend knee hip directly over the bent knee. Press your straight foot down strongly to activate your inner thigh. Relax and repeat a few times then switch sides.
After a few repetitions then go wider into the stretch with your hands on the floor. Slowly press the straight leg foot down into the floor so that your inner thigh activates, and then slowly relax. Repeat.
Another leg strengthening exercise that can work wonders on your glutes is bridge pose.
Lying on your back with feet on the floor and hips lifted, focus on pressing your feet strongly into the floor to press your hips higher. Keep your hips lifted and then relax your feet. Repeat a few times.
To increase the leg strengthening action, an option is to press down strongly through the shoulders. Then press down strongly through one foot and then lift the other foot.
You'll probably find that when you press down with one foot the opposite shoulder will also strongly press down.
When you lift your leg try to keep your hips from sinking.
To exercise the hip flexors of the lift leg, reach it straight up to the ceiling then work at pulling it back (towards your head.)
So that you don't lose awareness of your supporting leg:
This next seated leg strengthening exercise I'll call a seated get up.
If you have knee problems either leave this leg exercise out or do it with awareness. It can be stressful on the bottom knee, so be careful of your foot position (point the bottom foot!) when leaning forwards. It can also be stressful on the top knee, so brace your heel and/or use your hands to help, particularly when lifting the bottom leg.
Start with one leg in pigeon position (the bottom leg) and the other leg on top with the foot just in front of the bottom shin.
To protect the bottom knee when you lift your hips, point your bottom foot!
Place your bottom leg hand on the floor slightly behind your hips.
Once you are comfortable with this try it without using your hand. Again, be aware of your knees. Desist if you feel they are in danger.
Next you can add a leg lift.
This will strengthen the front leg, including the calf (if you stabilize the heel and back of the knee), quadriceps, and potentially the glutes.
Start in the hips lifted position.
Try to activate the calf and back of the knee of the top leg. Then press down through your foot strongly. Relax and repeat a few times.
Now, place your hands on your top leg to help support your body weight. Activate your calf, then after pressing your foot into the floor, press your hands down strongly against your leg. Then lift your bottom leg. Lower the leg and relax. Repeat a few times, then switch sides.
Then try it but starting from the floor. Use your hand if needed to lift your hips, then put your hands on your top knee prior to lifting your bottom leg. Put your hand back on the floor prior to lowering your hips.
Do all actions slowly and smoothly. As you get more comfortable and if your knees feel safe, try doing one stage at a time without using your hands.
After the last rep you can simply stand up.
This video from my youtube channel goes through all the steps.
One way of thinking about this next exercise is as a way of practicing switching from lunging on one side to the other. (The previous exercise is so that you can work towards standing or sitting just using the strength of your legs.)
From the previous leg strengthening exerise, touch the back foot to the floor.
Once you are comfortable you can combine this exercise with the previous one.
A variation of the previous two exercises is to touch one knee lightly to the floor while keeping the foot lifted.
This is something you can work towards gradually. Go only as low as feels comfortable on your knee.
One of the ultimate exercises for body weight leg strengthening is the pistol squat. Here's some suggestions for Learning the Pistol Squat step-by-step.
More ways that you can use both friction and pressure to strengthen the legs and arms are included in the Frictional Arm and Leg Strength program.
This program not only helps you to improve strength but also body awareness and is available as a set of videos or as a PDF (or both).
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.