In reclining half hero pose, you lay on your back with one shin folded to the outside of the thigh. Ideally both butt cheeks are resting on the floor.
The process of laying back can be painful and so the first step in working towards this pose is to practice it while sitting upright.
You may find that your hero side butt cheek doesn't touch the floor and so your first goal can be that of letting your hip sink down inside your hero leg.
I had the same problem when I first started and a teacher told me to move my foot out to the side and let my hip gradually sink down.
To speed up the process you can practice sitting up tall and then relaxing in time with your breath. As you sit up tall press down with your straight leg so that you push your weight over your hero leg helping the hip sink down. Then relax and slouch and let your weight move towards your straight leg while you exhale.
To sit up even taller you may find it helps to interlace your fingers and push your palms up towards the ceiling.
Once your hero side hip or butt cheek starts getting closer to the floor your can start working on laying back. You may find that laying back adds even more weight to your hero leg hip so even if your butt doesn't touch the floor, laying back may help.
You may find it easier to bend your straight leg arm. Lean back on your straight leg side, and once that elbow is on the floor, then try to get your hero side elbow on the floor.
You can make yourself more comfortable by laying back on some blocks or a bolster.
To lay all the way down you might first try putting the crown of your head on the floor, and then partially propping yourself with your head and neck then move your arms out to the side to lower your ribcage.
For myself my left quad tends to be a little tight and so when doing reclining half hero pose with my left knee bent my knee tends to lift.
The first step is for me to lift my hips and try shifting them either left or right or slightly forwards or back relative to my knee. I can usually find a position for my pelvis (relative to my knee) that makes it easier for my knee to sink down. Generally I like to think of this as creating room in the hip joint. By moving my pelvis relative to my half hero knee, I can find a position where my hip is open and thus facilitate my knee lowering to the floor.
Another trick is to press down with the hero foot. This action, pressing down, adds tension to the leg and that tension can often times be enough to make my knee sink down of its own accord.
Once you are on your back in reclining half hero you can reach one or both arms back. I like to focus on my lower back ribs (near the kidney area). Instead of reaching just my arms back, I reach my lower back ribs away from my pelvis also. The feeling is like I'm lengthening (or trying to lengthen) my lower back.
You could also first reach just your hero arm back. Reach your leg forward at the same time. Then when you reach your other arm back focus on lengthening both sides of your body. Reach your arms back and your legs forwards.
For a change in reclining half hero, and to increase the quad stretch, bend your other knee, place the foot on the floor and lift the pelvis. Try to keep your half hero knee on the floor.
To increase the quad stretch in reclining half hero even more hug the lifted knee to the chest.
You may find that you tip to the side when doing this so brace your self with your lifted leg elbow.
Another option is to straighten the lifted knee. Try grabbing the knee first and then gradually work your hands towards your foot.
You may find this variation easier if you grab your foot with your opposite hand so that you can brace yourself with your free hand.