In order to access the appropriate muscle groups, it may be helpful to think of Eka Pada Bakasana II as Bakasana (Crane Pose) on one side and Tittibhasana (Insect Posture) on the other. I recommend practicing both of these asanas individually to explore these actions before combining them in Eka Pada Bakasana II.
Enter this variation of One-legged Crane from Crane Pose by dropping the hips slightly as you extend one leg straight. Hug both knees firmly against the upper arms and engage mula bandha (root lock) and uddiyana bandha (navel lock) by lifting the pelvic floor and sucking the navel up and in to create a sense of lightness in the body. As in all asanas in which we carry weight on the hands, remember to spread the weight evenly across the entire surface of the palm and engage the fingers (think: "suction cup fingertips") to avoid collapsing onto the heels of the hands and straining the wrists.
Advanced practitioners may begin in Salamba Sirsasana (Tripod Headstand), then push up to Bakasana and take Eka Pada Bakasana II from there. To exit the pose, either move back through Bakasana to Salamba Sirsasana, or stretch the bent leg back and bend the elbows to balance in Eka Pada Koundinyasana II, then jump back to Chaturanga and take a vinyasa.
*See Eka Pada Bakasana I