Frog on the ledge, contemplating life 
Ah, downward facing frog. So deceptively simple. So excruciatingly painful. The thought of sitting through another minute of it makes me consider just ending it all.
Does absolute wonders for your hips though.
Frog Pose – Overview
Not to be confused with all the other frog variations out there, downward frog (Adho Mukha Mandukasana in Sanskrit) is an intermediate yoga pose that belongs to the hip openers category. This asana targets glutes & hip flexors and quadriceps, and also involves ankles and knees muscles. Frog improves circulation in the hip region; opens hips and groins and also removes stagnant emotions.
Benefits of the pose includes:
– Relieves anxiety, stress and mild depression
– Opens the hips, inner thighs and groin
– Opens the chest and shoulders
– Soothes menstrual cramps
– Aids in digestion
We get what the frog is good for. And I know as well as the next guy how to ape our pretty yoga instructor and plonk the old tired body into some kind of configuration resembling what I see in front of me. Monkey see, monkey do. But that’s no way to practice yoga. Brainless parroting will only get you (and me) so far, and is a surefire one-way ticket to getting yourself injured. Just look at the beautiful lady over there. Imagine yourself exactly in her place, in that exact position. An accidental slip (&/or maybe a helping push), and snap goes your delicate groin muscles, or pop goes your hip sockets as they dislocate. Marvelous right.
< One of the seven natural wonders of the world. 
Oh baby  >
It’s All in the Hips
To start off, ease yourself into that frog position. Not too hasty now, I don’t want to have a lawsuit in my hands. Start off at tabletop position, then slowly open up your knees (abduction of the hip joint) keeping your knee joints flexed at 90. Keep going and you should start to really feel it in your groin/inner thighs. Yep, it’s those muscles. Stay there for a couple of minutes and I wager you’ll have a slight bit of trouble getting out.
The key movement happening here is abduction (moving thigh laterally away from pelvis) of the femur (thigh). The muscles normally engaged in effecting this movement are the abductors; gluteus medius and minimus, obturator externus, gemelli, and sartorius.
< Key Thigh Abductor Muscles 
Key Thigh Abductor Muscles – Sartorius  >
Newton’s Third Law dictates that every action has an equal and opposite reaction. To counteract the abduction of your femur, the adductor group of muscles (adductor brevis, adductor longus, adductor magnus, pectineus, and gracilis) would have to hold the stretch else your femur will abduct way beyond the bounds of what the body is capable; tearing your iliofemoral ligaments and dislocating your socket hip joint. Sounds hunky dory aye.
Key Thigh Adductor Muscles 
The typical frog pose is done in a static passive stretch with gravity doing the work on pulling down your hips. The abductors stay loose, the adductors pulls taut. You maneuver yourself into that position and hang on for dear life.
But say you’re an independent autonomous sovereign individual who refuses to let yourself be pushed around by others. You won’t take crap from anyone, no matter whether it be the cops, society, dishonest politicians, old college professors, or even gravity itself, that cheeky bastard. You take your destiny into your own hands. No, for you, it’s gotta be a (static) active stretch.
All those strange sounding abductor muscles; gluteus medius and minimus, obturator externus, gemelli, and sartorius. Those funny muscles you never knew you had. Engage the lazy buggers to bring your adductors even more torment. It’s fine not to remember all these high falutin latin sounding names. Focus on that same feeling when you perform side leg raises while standing up, do that same thing while you’re in that frog pose. Really think about contracting the hell out of those abductor muscles. That my friend, we call self-empowerment.
I think some people call it masochism.
Bit more on Bodily Positioning in the Frog
I think the basic positioning involved in the final pose is pretty straight forward. 90 degree flexion of both the thigh as well as the knee. Hands and elbows both placed firmly on the ground in support of your upper body weight. You’ll want these upper limbs nice and grounded to help facilitate minimum distractions for the heavy lifting below.
For my more technically inclined readers, you’d probably also want to work on correcting any excessive anterior pelvic tilts by tucking in your navel. And of course, make sure to correct any unevenness between the left and the right by ensuring your sit bones and level with the ground (you can get the help of a friend to check this). I’d wouldn’t think you’ll have much freedom of movement with regard to rotation of the femur (thigh) if you follow the 90 degree by 90 degree pelvis-thigh-calf configuration. Your calves might be slightly rotated externally depending on how flexible you are in the hips. It should be fine to retain your calves and feet at their natural positions (slightly externally rotated and neither dorsi nor planta flexed respectively) to better support the work around your main focus of the pose; the abduction of the femur (thigh) itself.
Honestly, while not ideal, I’d normally just default to the monkey-see-monkey-do mantra to begin with. Your awareness of(im)proper positioning should come naturally through the proper feedback channels (complaints, scoldings) after awhile.
A Final Word: Joints and Ligaments.
We spoke a little on hip joint dislocations just now. Flexibility is just about always limited by both your muscles as well as your ligaments. Muscle flexibility can definitely be improved through diligent training in the short-medium term, but you’d also want to play the long game in conservative, disciplined progressions to safely stretch out your ligaments. The ligaments will definitely stretch out as you keep at your practice. Just clear your thoughts, listen to your body, and always remember to breathe.
Seriously can’t get over these insane breeches. What the hell man. 
: The Key Muscles of Hatha Yoga, 3rd ed, Bhanda Yoga Publications, Ray Long