Named for the sage Galava, this pose is usually referred to in English as flying pigeon pose, which makes sense if you look at the position of the top leg and notice as well that the rest of you is… not on the floor.
In the book of Tanya, there are three important keys to getting this pose: bent arms, getting the foot and knee as deeply into the armpits as you can, and pressing the shin of the top leg away from you. If you struggle with hip mobility, this pose may be a little down the road for you, but doing all the preparatory work for the pose is the way to eventually get into it. If you are a person with excess hip mobility, your challenge will be to balance the external hip rotation that is easily come by with intentional opposing internal rotation to keep the muscles around the join active. This will not only give your pose buoyancy and dynamic energy, it will strengthen the muscles around the hip joint and protect it from long term wear and tear.
To open your hip joint ahead of time, try runners’ stretch, hanumanasana (if it’s available to you, or whatever variation you are working on), seated or standing baby cradle, pigeon prep, and might as well throw a bhakasana or two in there to get used to the feeling of being in the air. The work of pulling the belly in and up and inflating through the back of the ribcage is helpful for EPG as well.
Once you’ve prepped for the pose, begin by standing in hangman pose with one ankle resting on the opposite knee, creating a figure 4 shape with your legs. Squeeze your inner thighs in toward each other, flex the little toe side of the raised foot toward the outside of the knee (protecting your knee joint, just as you do in Pigeon Prep) and bend forward, bringing your fingers to floor as you bend your standing knee. 
If you wish, this is a fun opportunity to practice toe stand, a la Bikram. 
Whether you do toe stand or not, get yourself back into the previous pose, fingers to floor, and tuck your shin as deeply up into your armpits as you can, and flex your toes strongly so you wrap your toes around the outside of your upper arm. BEND YOUR ELBOWS, as though you were doing a pushup, or Chatturanga Dandasana. Tilt your weight forward, head moving floor-ward. PRESS YOUR SHIN DOWN into the shelf you have created for it by bending your elbows. With your weight forward in the direction of your head, lift your back foot up off of the floor and play with just balancing on your hands. 
KEEP PUSHING your shin down into the back of your arms. Reach through the sole of your top foot, straightening your leg. Fill and open your ribcage, becoming buoyant in the same way you do in Bhakasana. To challenge yourself, rather than lifting your hips high away from the floor, try to keep your hips closer to the level of your shoulders. Pull your hands toward your feet, protecting and strengthening your shoulder joints. 
For more in-depth discussion and background into Eka Pada Galavasana, please visit the following link: http://www.yogitimes.com/article/eka-pada-galavasana-flying-crow-pose/
Enjoy!!
