There are many ways to come into and out of yoga postures and sequences of postures. Below is one way to try a chandra namaskar. It is based on the classes I have taken with Yoga Synergy and you should go to their website to get material directly from the source and understand this is my interpretation only.
And while I mention it as based on the Yoga Synergy style (based on the emphasis on moving the sitting bones forward), I note my teacher Paddy McGrath also encourages similar movements (but without the same anatomical instructions) in the classes I have had with her--particularly the actions of bhujangasana, which requires postural firmness in the belly while simultaneously keeping the spine long rather than squashing it.
This sequence is practiced with natural breathing; breathing into the belly. The belly is made firm by the posture, which, in this case, is caused by moving the sitting bones forward and top of the pelvis back. This action also creates length in the lower back, which tends to get squashed in most people.
What I try to distinguish between as I practice this sequence is a movement of my spine versus a movement at the hip joint. You will see that from standing, I first bend the spine (from the navel upwards), then I bend at the hips and knees to come to the floor. I don't worry about straight legs here. I am more concerned with the movements of the spine.
You will see that I step back into a low lunge. Before I stand up I firm the belly by pushing the sitting bones towards the front heel. Then I stand up.
You will see in kneeling plank I use the same action of pushing sitting bones forward to cultivate a firm belly but I still breathe into it so that I am calm.
You will also see that in the second cycle I come from kneeling plank into bhujangasana. That transition is really important. I am moving into a backward bend but I do not stop pressing the sitting bones forward. Look at this section really closely. You will see that the length in my lower back is maintained. The sitting bones continue to push forwards. If I let my bum stick up in the air it will squash.
You may not be able to lower your pelvis to the floor as much as I am. But lowering it is not important here. What is important is the length of your spine. Make that your focus.
When I cannot move forward anymore then I lengthen the front of my body without sticking my ribs out or squashing the back. In this way I feel freedom. I should mention the action of the armpits is strong here, which you cannot see, and they are pressing down and back (like I am trying to pull my hands back to my hips).
When I move back into kneeling plank I don't let the lower back sag.
Throughout this sequence I pay attention to my neck. I make sure it is not squashed and is in a position where it feels long and free.
In the second cycle you can see I try to maintain the feeling of kneeling plank and tip-toe my feet towards my hands. Here I was just playing around with maintaining that feeling while putting weight through my arms. Some people might lift to lolasana (take their toes off the ground and hover) or even a handstand if that is available to you. It is not available to me so I just stay at the level I am at, be content with that, and breathe.
Move slowly through this sequence. Don't practice it if you are unsure or if anything does not look or feel right to you.
May your practice be peaceful and happy!