To work toward a one legged lying quadriceps stretch you can start with a one legged kneeling position. Bend the other knee and place the foot against the inner thigh of the kneeling leg.
If you have tight quadriceps, you may find that you have to lean away from your kneeling leg.
To stretch your quadriceps in this position, begin by using your arm to push yourself gradually upright. As you do so focus on activating the quadriceps or knee of your kneeling leg (make the knee feel "strong"). You could also focus on activating the hamstrings.
This is a continuation of the kneeling quadriceps stretch.
Activating the quadriceps while stretching it might seem like you are resisting the quadriceps stretch. But muscle tissue can lengthen while active (it just has to be activating with less force than the force it is working against). In either case, notice the feeling in the knee and notice whether or not activating the quadriceps or knee or hamstrings helps you to come comfortably more upright.
Note that to push yourself upright you can use your hand and arm as mentioned. Or you can press your other knee down into the floor.
Once you can get comfortably upright with this leg position you can stretch the quadriceps stretch further by sinking your kneeling leg hip to the floor. To do this you can add weight to the stretch by bending your spine towards to your kneeling leg side. Initially start with your hand on the floor to help support your body.
Focus on activating your knee or quadriceps and then relaxing. The activation is to create stability in the knee joint. Practicing activating and relaxing develops control and also awareness, the ability to feel your quadriceps and knee joint.
Repeat a few times, and if comfortable with the action then see if you can relax your supporting arm during the activation phase. Try to relax the arm completely while your quadriceps is engaged, then if you feel comfortable, lift your hand off of the floor. Then, put hand back down (re-support your body using it) before relaxing your leg.
Once comfortable with this then see if you can relax your leg while keeping the arm lifted.
Another option that strengthens the knee and/or quadricep is to reach one arm and then both arms to the side while keeping your leg active. This strengthens the quadriceps because it has to work against more weight, the weight of your arms.
If the hip on your kneeling leg side is closer to the floor or, better yet, touching the floor, then you are ready for the lying quadriceps stretch.
The lying quadriceps stretch can be done one leg at a time. To begin with, have one leg in the kneeling position and the other leg straight. If in this position you find that your kneeling leg hip lifts, then here again you can use your hand to support yourself initially when leaning away from the kneeling leg. Then use it to help push you upright. Then, as before, try using your non-kneeling leg to get you (and keep you) upright. To work towards this, practice pushing down with the straight knee foot for support. Press down and upright yourself, and then relax.
Place your hands on the floor behind you to lie down. If you find your quadriceps is extremely tight experiment with activating it and relaxing it. Again, a simple technique is to push down with the shin or foot of the kneeling leg. Make it feel as if you are trying to come out of the kneeling position. While doing this you may find it helps to move your bent knee outwards or inwards slightly. See if you can find a position where your knee and quadriceps both feel comfortable.
As you lie back you may find that your lower back feels like it is being pulled forwards. One action to try to relieve this is to work at drawing your back ribs away from the back of your pelvis, as if to lengthen your lower back. Another option is to engage your abs. Try to create a line of tension between the front of your ribcage and the front of your pelvis. Or imagine beginning a straight legged sit up.
You might also find it helpful to reach through both knees, as if trying to push them away from your hip sockets.
After some practice you may find that you can go back on to your elbows. From there you can work at getting the top of your head to the floor in which case you can try pressing it into the floor in such a way that your head and neck helps to support the weight of your upper body. You may then find that you can move your arms in such a way as to gradually lower the back of your ribcage to the floor.
Generally, the lower you go, the easier it is to experience lumbar spine discomfort. To that end try activating the quadriceps, or reaching through the knees and/or activating the abs. Experiment till you find a solution that doesn't cause your lower back to feel like it is going to be pulled apart. Failing that there are other positions for stretching your quadriceps.
If you can do the lying quadriceps stretch successfully and comfortably, a few options for increasing the stretch as follows. Bend the straight knee and place the foot on the floor. Use this leg to lift your hips a little. Work at keeping the kneeling leg knee on the floor as you do so. From here a deeper quadriceps stretch involves hugging the knee of the non-stretched leg to the chest. To take the stretch even further, try doing this with the knee straight.