As the name suggests, pigeon yoga hip stretch is a stretch for the hips.
In this version of pigeon yoga hip stretch, rather than resting the front-leg-hip on the floor, lift it so that the pelvis is level from left to right.
At the same time make sure that your back leg knee points straight down.
(To lift the hip use your leg muscles to press down with your front knee.)
With pelvis level from side-to-side, lay down and reach your arms forwards.
Create space in the pose by reaching your spine and arms forwards. At the same time reach your pelvis and back leg back, away from the front knee.
Both of these actions add weight to the back leg side of the body. Because of that, vary the downward pressure of the front knee so that you keep your pelvis level. Try to keep your pelvis level from left to right as the weight of your lifted leg and arm cause your body to sink.
In the pictures I have the top of my back foot on the floor.
You can do pigeon yoga hip stretch with the top of your back foot flat on the floor or with toes tucked under.
In either case you may find that you have to press the foot down to lift the back knee and keep it lifted.
Generally the hip stretch deepens the further forwards you have your front foot (increasing the angle between shin and thight).
The ideal is to have your front shin parallel to the front of your mat so that the front knee is open to almost 90 degrees. This can be challenging (and painful.) So I like to work towards this foot position gradually.
In all variations move slowly, particularly when sinking your chest down. If your knee hurts, change the way that you move into the pose. Try moving your pelvis slightly forwards or backwards (or to either side) till you can find a position where your knee doesn't hurt. Get used to moving into and out of the pose slowly.
If you find it difficult to keep your front leg hip lifted, particularly in the final repetition of pigeon yoga hip stretch, you may find it helpful to start with the front-leg-arm to the side. Then as you lower your torso and as you find your way into the stretch you can gradually move your arm forwards.
When lifting the back-leg-arm, particularly in the final version of the pose, you may find that it helps to push your front leg knee down into the floor. You may also find that it helps to press the foot down. Or you may find it helps to do both but with slight differences in pressure between the foot and the knee.
You might also find that it helps to shift your torso slightly one way or another.
When lifting your back-leg-arm, rather than suddenly lifting the arm, try to pressurize your foundation where necessary (press down) and slowly lift the arm. Likewise with the back knee. Instead of suddenly lifting your back knee, notice the feeling in your back foot and pelvis as you slowly lift it. You can then notice the sensation of "adding weight" to the pose.
Variations of Pigeon Yoga Hip Stretch include upright pigeon Hip Flexor Stretch and Screaming Pigeon Hip Stretch.