When working with beginners, I usually like to go through a progressively harder set of side plank preparation exercises.
One reason for this is to train shoulder awareness so that they can effectively stabilize their scapula. Another is so that they learn how to use their legs to lift their hips, first with knee bent, then with knee straight using the top leg (for the inner thighs) and then the bottom leg (for the outer thighs).
In combination with this another aspect is learning to activate muscles at the front of the lifted leg (quadriceps and hip flexors) followed by the muscles at the back of the leg (hamstrings and possibly gluteus maximus.)
One way to do this is to lift the knee or leg without holding on to it.
For each set, I like to repeat both sides before moving on to the next set.
Generally I like to start with bent elbows so that the focus is on the shoulders (as opposed to the wrist.) Focus on using the shoulder to push the ribcage up.
With shoulder lift the next step is to use the outer thigh muscles to lift the pelvis. Keep the shoulder engaged and from there reach the top arm up.
Next lift the top knee and point it upwards. Here you can practice engaging the quadriceps. If that's no problem try to straighten the knee without holding on to the foot.
For side plank with the elbow straight try pressing down with the tips of the fingers and the heel of the hand. You can also try pressing the hand outwards as well as downwards. Lift the hips and as before lift the top knee straight up. It'll be harder this time because of the higher angle of the body. Pause for a few breaths then if you like straighten the knee without holding on to the foot.
With hips lifted lift the top foot, straighten the knee and place the foot on the floor. Press the top foot into the floor so that the leg feels strong then lift the bottom shin. Keep the shoulder active.
From the previous position set the bottom foot on the floor either in front of or behind the top foot. Lift the top knee.
From the previous straighten the top knee. If you need to, bend the knee to grab the side of the foot or big toe. Then straighten the knee. Activate the back of the thigh as if trying to pull the foot away from the hand.
As a yoga teacher, I'm constantly exploring new exercises, new ways of doing yoga poses.
There is no single "right way" of doing a yoga pose. Instead, there are options. And the better you are at "feeling" your body, the better you can get at choosing the right option for your body as it is now.
For any technique, the point of practice is to learn feel it and to control it, so that it can be used without thinking about how to use it.
And that is more or less the approach taken in all of my ebooks and videos. They help you to feel your body and control it so that you can work towards using it effectively in anything that you do.