So you might have clicked through to this post wondering WHY someone would want to learn headstand, so I'll address that question first.
In general, inversion poses (where the head is down and the feet are up) rejuvenate the legs and bring them a deep sense of rest. These poses are especially good for people with circulation problems, varicose veins, or restless legs syndrome, as well as those who spend a lot of time on their feet. Having the head below the heart brings fresh blood to the brain, since it flows easily there instead of the heart having to pump it upward. In general, inversions improve the effectiveness of the lymphatic system to flush out waste products and invaders in the body. Going upside-down also helps the digestive system, reversing the direction of gravitational forces to help remove blockages—although it's best to wait at least a couple of hours after a meal to do this pose.
There are a few inversions that provide these benefits and are essentially foolproof, not requiring much learning or instruction—such as Viparita Karani (legs up the wall). But headstand has some additional benefits that make it desirable to learn and, in fact, one of the most important poses in my own daily practice.
Balancing on the head stimulates the pineal gland, which regulates the sleep-wake cycle. Because it secretes melatonin and serotonin, having a well-functioning pineal gland is important for preventing conditions such as insomnia and seasonal affective disorder. Headstand also acts on the pituitary gland, which regulates many endocrine processes in the body, including thyroid function and reproduction. For this reason, headstand contributes to a well-balanced endocrine system.
In addition, with proper alignment, headstand stimulates the vagus nerve, which is the longest of the cranial nerves and activates the parasympathetic nervous system, interrupting the fight-or-flight response and inducing a state of relaxation. The vagus nerve regulates inflammation in the body, as well as electrical impulses to the heart.
If you're convinced that headstand is something you'd like to learn, here are my best tips for learning it effectively and safely. (Ideally, you would learn it in class under the supervision of a teacher, but based on my experience teaching yoga, I know many students attempt to teach themselves, so I would rather provide a resource to help you do it safely than just pretend people aren't trying this on their own outside of class.)
STEP ONE: First, build strength and awareness in your shoulder and neck muscles. In Adho Mukha Svanasana (Downward Facing Dog), work to rotate your arms and press back from the legs and hips to create space around the neck. Work on similar actions in Dolphin pose. Practice Prasarita Padottanasana to get comfortable placing some weight on the crown of your head; in this pose, make a point of lifting the shoulders away from the ears.
STEP TWO: You'll also want to get comfortable going upside down in poses such as Uttanasana, as well as Adho Mukha Svanasana and Prasarita Padottanasana (discussed above). It may sound simple, but your nervous system needs to get used to seeing the world upside down. Headstand will be that much easier (and less scary) if you've already spent a lot of time seeing the world topsy turvy.
STEP THREE: Work on poses in which you lift and extend through one leg at a time, such as Virabhadrasana III and Ekapada Adho Mukha Svanasana. Focus on strongly lifting and extending the airborne leg, so much that you feel some of the weight is being taken off the parts of your body that are touching down, due to how hard your leg is working. This is exactly the kind of action you will need to come up into headstand. As a beginner, you'll be coming up one leg at a time, and you should work to extend one leg so strongly that it feels like it pulls the other one up after it.
STEP FOUR: Work at the wall or using a chair (or both). Watch my YouTube video that shows how to come into headstand at the wall, including key alignment points to protect your neck. With practice, you will want to come away from the wall, since leaning your feet that far back pulls you out of alignment and can subject your neck to strain, especially since we tend not to use the core as effectively if the feet are resting and don't have to be held up to keep from falling backward. But at first, the wall is a wonderful tool for alleviating fear and for keeping the neck muscles from bearing too much load before they are strong enough to take it. Also check out my YouTube video that shows how to step up onto a chair before coming up, and thus remove some of the core work (and swinging in the spine and neck) and allow you to come up with control even as you're still getting the hang of your alignment in the pose. See also my videos explaining proper hand position and head position for this pose.
Please don't hesitate to reach out to me if you have any questions while learning this pose! Yoga is my passion and I love to answer questions about it.