Sun Salutation A (Surya Namaskara) has ten "breath-linked" movements. Each of these movements is done with either an inhale or an exhale.
In the picture, odd numbered moves (red) are done while inhaling. Think of the inhales as the "working phase" of the breath.
Even numbered moves (blue) are done whil exhaling. Think of exhales as the "relaxing phase" of the breath.
Here's an overview.
Start in a standing position with:
While inhaling pull your ribs and head up and away from your pelvis.
While exhaling, relax your head forwards and allow your ribs to sink downwards. Make both actions smooth and slow.
To make learning these steps easier you can break Sun Salutation A down into a series of mini-sun salutations.
In the first (and last) position of sun salutation A you stand with your feet together.
Notice your heels, forefeet and toes and feel how they press down into the ground.
While holding mountain pose,
To lengthen, pull your head back and up and lift your ribs. To relax, reverse these actions.
Once you have the hang of lengthening your spine and relaxing it,
Continue to lengthen your spine as you lift your arms up and make your arms feel long as you do so. Slowly try to touch the ceiling as you inhale and let your bones relax down to the ground while exhaling. Read about activating your trapezius muscle if you have trouble touching your hands together over your head.
Next bend forwards and place your hands on your knees or on the floor. Bend your spine forwards.
As you inhale straighten your spine and move your ribs away from your pelvis.
If you can't keep your hands on the floor as you do this, reach them back and make them feel long as you do so.
Slowly relax and allow your spine to bend forwards as you exhale.
Now you can practice your first mini-sun salutation. From standing:
(Note that there are 6 steps in the mini sun salute above. Count those steps to yourself as you do the movements.)
From the "spine reaching forward position" above, place hands on the floor and step your feet back to plank. Bend your elbows and lower to chaturanga dandasana or simply slowly lay down. Try to do this smoothly on one exhale.
Then stand back up and repeat.
Inhale reach your spine forwards, exhale and step back and lay down. Stand back up again.
For the next exercise, start from the laying down position from the above step. You can lift up into upward facing dog or if that is too uncomfortable replace it with either cobra pose or locus pose.
Focus on using your spinal erectors to bend your spine backwards.
Inhale lift into upward dog, and then lay back down again. Repeat this a few times.
Adding on to the previous exercise, I'm going to add an extra step which isn't normally included in a sun salutation. Normally you exhale back into downward dog both in Sun Salutation A and Sun Salutation B. Instead from upward facing dog, exhale to cat pose and then from there inhale into downward dog.
When inhaling into downward dog focus on using your arms and spine to push your hips back and up. (In the first movement you reached your arms and spine up. In this movement you can try to create the same feeling. But since your hands are on the floor you can focus on pushing your pelvis back away from your hands.)
The next sun salutation A mini-sequence is as follows:
From laying down,
After repeating this a few times you can experiment with this mini-sequence:
The next step is to practice stepping forwards from downward dog.
From downward dog, move your shoulders forwards over your wrists as you exhale. Press your fingers tips into the floor as you do so. Keep your hips high. As you inhale walk or jump your feet forwards, between your hands. On the same inhale reach your spine forwards and lift your hands if you need to. Keep your knees straight.
Step back to downward dog and repeat this a few times.
Next, after reaching your spine forwards, exhale and bend forwards. Then inhale and lift your arms. (Touch the ceiling.) Exhale and lower them to your side.
Practice this whole sequence from downward dog. The action a lot of people miss out is "reaching the spine forwards" on the same inhale as they step forwards.
From the bent forwards positioin practice the following steps:
If you like the cat pose insertion between up dog and down dog then the sequence will look like this:
Now you can practice the whole of sun salution A. Remember that inhales are odd numbered while exhales are even numbered. There are 10 moves in total so that if you count moves and find that you have more or less than 10 you've made a mistake:
Once you are comfortable with the sequence of moves you can hold down dog for five breaths. Then continue the count as you step forwards (7).
Here's the sequence with cat pose inserted
Note that the numbers are a handy way to check your moves when you are first learning sun salutation A (or its variation).
If you like you can hold any of the poses for a few breaths. Just make sure that you move into the next pose with the "defined" breath phase (either an inhale or an exhale as required.)
One way of approaching sun salutation A is to stay as relaxed as possible as you move. Generally, the more relaxed you are the more you can focus on feeling your body. You can notice excess tension and release it. You can then work on using the minimum amount of effort to do what you are trying to do. This can be especially true if you want to feel relaxed and energized after you practice instead of worn out and tired.
So that it is easier to use your breath, focus on gradually lengthening as you inhale, in whatever pose you are doing or moving into. Relax as much as you can while exhaling while still holding the shape of the yoga posture that you are doing.