One of the best ways to open the hips and prepare for Eka Pada Raja Kapotasana (One-Legged King Pigeon Pose) is through a supine modification called Eye of the Needle (sometimes called Dead Pigeon). This pose is great for first timers as well as experienced yoga students. As you move through this variation, and then toward the final pose, make sure that you alternate sides so that your body can unfold evenly and progressively.
To begin, come onto your back with your knees bent and your thighs parallel and hip-distance apart. Next, cross your left ankle over your right thigh, making sure that your anklebone clears your thigh. Actively flex your front foot by pulling your toes back. When you do this, the center of your foot will line up with your kneecap rather than curving into a sickle shape, which can stress the ligaments of the ankle and the knee.
Maintaining this alignment, pull your right knee in toward your chest, thread your left arm through the triangle between your legs and clasp your hands around the back of your right leg. If you can hold in front of your shin without lifting your shoulders off the floor or rounding the upper back, do so; otherwise, keep your hands clasped around your hamstring or use a strap. The goal is to avoid creating tension in the neck and shoulders as you open the hips, so choose a position that keeps your upper body relaxed. As you draw your right leg in toward you (making sure to aim it toward your right shoulder and not the center of your chest), simultaneously press your left knee away from you.