Before attempting this, make sure you are able and confident with doing Sun Salutation A.
So you've done several rounds of Sun Salutation A and are ready to move on. Sun Salutation B (Surya Namaskara B) has a longer sereis of poses than the former as well as the addition of strength moves. Combined, they are a workout and therapy, both strengthening and balancing the body.
Begin Sun Salutation B (SSB) at the end of your last Sun Salutation A (SSA).
Inhale. Lift your arms as you did at the end of Mountain Pose/Tadasana but squat as you do so, keeping your heels on the floor, chest lifted, back straight, gaze through hands. Holding mula and uddiyana bandhas helps maintain a straight back. Don't worry if you can only make it down a little bit, as you both strengthen and loosen, you'll be able to go deeper.
Exhale. Same as Sun Salutation A (SSA).
Look up. Inhale. Same as SSA.
Exhale (Four-Limbed Stick Pose/Chaturanga Dandasana). Same as SSA.
Inhale (Face Up Dog Pose/Urdhva Muka Svanasana). Same as SSA.
Exhale. Face Down Dog. Press yourself down and back in to this position. Refer, if necessary, to SSA for instructions.
Inhale. Bring left foot up and place ith between the hands. Right foot remains behind and turns outward roughly 45°. Keep right knee drawn upward by flexing right quadricep. Ideally, the left knee should be directly over the left ankle and in line with the foot with the left thigh parallel to the floor. Do not worry if this doesn't describe you. Do your best, as always.
Remember, this is supposed to heal you, and misalignment of the knee-ankle-foot combo will result in stress. Do not let the knee drift out past the foot or off to either side in an attempt to bring the thigh even with the floor and feel a good stretch. It's a bad stretch, believe me. In the beginning, pause to check your alignment. It is helpful to use a mirror for this or maybe have a friend watch and give pointers.
Inhale. Raise hands over head as in Four-Limbed Stick pose with gaze through the hands. Use your shoulders to push hands upward. Notice the similarity your upper body has in this pose with the initial pose. Maintain the same reach and straightness here. Of course, holding the locks will help.
The position you are in now is called Warrior I Posture/Virabhdrasana. It strengthens and aligns the hips, knees and shoulders.
With all that's going on here -- right leg straight with quad tight, right heel on floor, left leg knee-ankle-foot alignment, bandhas, lifting and straightening the spine through the shoulders and arms -- this is a tough pose to get right the first time. Please feel free to break it down and take one aspect at a time, perhaps focussing on knee alignment until that is perfect and then working on the arms and shoulders. It will take a while until the pose is pristine, that's why this is called a practice.
There's a temptation to hold this pose too long. Do not hold your breath here, but follow it and release the pose after the inhale.
Exhale. Swing hands to the floor, flat if you can. Don't drop your head. Gaze is forward. Straighten left leg. Drop to Four-Limbed Stick pose.
Inhale. Face Up Dog.
Exhale. Face Down Dog.
Inhale. Repeat Warrior I Pose, but bring right leg forward and keep left leg back. All instructions still apply, just switch sides. Don't hold your breath. Remember to inhale as you raise your hands and exhale as you bring them to the floor.
Exhale. Drop to Four-Limbed Stick pose.
Inhale. Face Up Dog.
Exhale in to Face Down Dog. Hold this pose for five breaths. Attempt ujjayi breathing. Walk feet or jump back to hands on the final exhalation.
Inhale. Look up. Keep those knees drawn up. Lift the chest and extend the back.
Exhale. Use your arms and shoulders to gently pull your head to your knees. Slightly bend your knees if you need to.
Inhale. Squat as you extend upward, keeping shoulders pressed against ears -- simultaneously lowering your butt as you raise your torso. Keep heels pushed in to the floor. You may find that you can go a bit deeper in to the squat now at the end of the series. Look up through hands.
Exhale in to Mountain Pose. Bring arms to side. Look straight ahead. Hold bandhas.
If you do no other yoga in your life, do a few series of Sun Salutation A followed by Sun Salutation B. For example, five Sun Salutation A's followed by five Sun Salutation B's every morning is a great way to start the day. Your coffee bill will decrease. You will feel both invogorated and noodly.
For a real test of strength, endurance and concentration, try longer sessions of each, like 20 SSA's and 10 SSB's. Not only is this an example of active meditation, but it is an exercise that you can do every day no matter who you are.