Setup and Key Actions
From downward facing dog, bring your left shin forward toward the front of your mat so that your left knee is outside your right wrist, and your left heel is in front of your right groin. Point your front foot, but flex the toes back toward you so that your foot is between flexed and pointed, and press the pinky-toe side of your foot into the floor so that your front ankle doesn’t sickle (collapse inward). If you want to deepen the stretch, widen your front knee out to the side while you work toward moving your front shin more toward parallel to the front edge of your mat (but avoid using your hand, which can twist the knee) and scoot your back leg back, until you get to a place where you feel a bit of a stretch in your front outer hip, but no knee pain. Press your fingertips into the floor beside your hips, and lengthen up through your spine. Draw the back-leg side of your belly toward the front-leg side and lift your back thigh up without lifting your back knee up. Move your front outer hip back. Keep the stability that you've created as you descend a little deeper into the pose—try moving your back leg back a little further. Keep your pelvis level.
You can keep your back leg extended (perhaps folding forward for eka pada rajakapotasana prep), or remain upright for the backbend/thigh stretch (eka pada raja kapotasana).
To set up for the thigh stretch, lightly squeeze your back-leg hamstrings and glutes as you draw your right heel in toward your seat and catch hold of the big-toe side of your foot with your right hand. You can choose to stay here and work with the thigh stretch, bending your right elbow and drawing your foot in toward you, all the while squaring your rib cage and chest toward the front of the mat. You can also work with flipping your grip here, spinning your fingers forward and your elbow up.
One Leg King Pigeon With a Strap
If you'd like to work toward catching your back leg behind you with your hands overhead (a variation in which both of your elbows will point up, requiring you to fully lengthen through your triceps), start with a strap. Make a generously sized loop with the strap, and wrap it around the sole of your right foot. Hold the loop in your right hand, palm facing up, and externally rotate (turn out) your upper arm. Keep the external rotation as you spin your right elbow up toward the ceiling. Then, reach your left hand up and back to catch hold of the strap as well. Keep your spine long, and turn from your belly to help keep your torso facing forward. Walk your hands down the strap as you continue to broaden your collarbones and lift your chest (you might touch your foot, you might not). As your chest lifts, move your head back to follow, keeping your neck long as you enjoy the backbend. Don't worry about touching your head to your foot. Just keep your backbend smooth and even.
One Leg King Pigeon Without a Strap
If you're able to walk your hands down the strap and easily catch hold of your foot, you may wish to try coming into the pose sans strap. From your pigeon thigh stretch with left leg forward, reach your left arm across your body and catch hold of the big-toe side of your right foot with your left hand. This keeps your foot in place while you get a good grip on it with your right hand. With the foot held in place by your left hand, externally rotate your right arm (just as you did when you were holding the strap), and wrap your right thumb around the pinky-toe side of your right foot, and your right fingers across holding onto the big-toe side of the foot. Once you have a good solid grip with your right hand, release your left hand as you spin your left elbow up toward the ceiling and your torso to once again face the short edge of your mat. From here, reach your right arm up and back, bending your elbow to hold onto your left foot with your left hand as well. Stay only as long as you can comfortably breathe before returning to your starting position and repeating on the other side.
If you're having difficulty keeping your pelvis level, place a yoga block, blanket, or end of a bolster under your front-leg hip.