The pose is actually very simple. Instead of having both knees straight as in full side splits, bend one knee and place it on the floor. The other knee is straight. Slowly work at sliding the foot of the straight leg and the bent knee apart.
You can start of with your hands on the floor with your elbows straight (as shown at right). As you go lower you can bend your elbows and place your forearms on the floor.
As you go lower yet you can go back on to your hands, and bend your elbows to lower your chest as if doing a push up.
With this last variation you can then repeatedly lift your chest to add weight to the inner thigh stretch and then lower your chest back down to rest and recover.
When getting into the half split position place your knee and the heel of your straight leg on the same line. Positio your pelvis in the vertical plane that passes up through the knee and foot.
In other words, when viewed from the side, your knee, foot and pelvis should all be aligned.
Viewed from the top your ribcage should be 90 degrees to your thighs.
Generally I suggest students fold over their matt and place their bent knee on that for comfort. Have the foot on the bare floor so that it can easily slide away from the bent knee.
As your foot moves away from your knee, move your elbows in the same direction so that you keep your body at 90 degrees to your legs.
As you can see from the picture above I'm not letting my head hang, nor is my chest sagging down between my shoulders. When doing this inner thigh stretch I'd suggest keeping your spine, and neck, long. And use your shoulders to push your ribcage up away from the floor.
To help relax your thighs so that you can stretch deeper practice activating them. As you inhale squeeze your inner thighs as it to pull your foot and knee together. At the same time lengthen your spine by pulling your ribs away from your pelvis and your ears away from your ribcage.
As you exhale you can relax your spine and also relax your inner thighs and let your foot slide away from your knee.
You could also activate your inner thighs by pressing your foot (and knee) down into the floor each time you inhale. Again relax as you exhale.
Or in either case focus on slowly activating your legs and then slowly relaxing the when you are ready.
The adductors are ideally the inner thigh muscles that you are stretching while doing this half split and also full split yoga poses. As you do half side splits focus on feeling your inner thighs. See if you can notice the line of greatest tension along your inner thighs. When you inhale focus on contracting the muscle that is most tense. Then see if it releases when you relax the tension.
Lifting and lowering the chest while in half side splits is a great way to add weight to the pose and increase the inner thigh stretch.
If you can't quite get your chest to the floor then prop it with blocks. (Sorry ladies if this isn't quite feasible for you. If you have room perhaps try perching the lower edge of your ribcage on the block or blocks.)
Prior to liftng your chest engage your inner thighs. Then slowly press down with your hands to lift your chest. Lower your chest and then relax your thighs. You can hold the raised position or slowly lift and lower either in time with your breath or as you see fit.
An additional way to add weight to half side splits, or if you like, leverage, is to move your hands or elbows, further forwards. In the first picture below my elbows are almost under my shoulders. In the second picture I've added weight by moving my elbows further forwards.
One way to cheat the stretch when doing half side splits is to move your hips further forwards as I'm doing in the picture below.
Sometimes it just happens. If you do get your hips to the floor by moving yoru pelvis forwards, then enjoy the sensation for a few moments and then lift yourself up and push your hips back a little bit. Wait till your hips sink down and then move back further.
I use this method in full splits. In full splits, so that I know my hips are in linke with heels I do it with my heels against a wall. When I feel my butt against the wall I know my pelvis and legs are in line.