First, make spiritual development a priority in your life. This is accomplished through Yama & Niyama.
Every one of the texts insists on this in one way or another, but the idea is most commonly reflected in the listing of Yama and Niyama, the ethical and self-disciplinary injunctions considered to be the minimum requirements for a yogic lifestyle. The number of injunctions differs - Yoga Sutra has ten, while Hatha Yoga Pradipika has twenty!
Second, cleanse, purify, and condition the physical body. This is accomplished by Shatkarma and Asana.
Shatkarma is a set of six types of purification practices, including nasal irrigation, intestinal flushes, and enemas. These basically get the body squeaky clean on the inside and outside, inducing both a physical and psychological state of purity.
Asanas are various bodily postures designed to condition and strengthen the body. The Asana practice is the first stage where the Hatha Yoga guidebooks start talking about the mental, emotional and spiritual benefits that come, in addition to the physical results of practice.
Third, develop control and regulation of the breath and energy. This is accomplished by Pranayama.
Pranayama is a set of breathing exercises designed to increase control over the breath, and, by association, the prana, or life energy of the body. One tenet of Hatha Yoga philosophy is that the mind and the breath are inextricably interlinked.
One is a mirror of the other. With that in mind, the emphasis on Pranayama makes sense from a yogic point of view - to control and still the breath is to control and still the mind, which is the ultimate goal of Yoga.
Fourth, activate latent Kundalini energy in the body to stabilize and energize the body & mind. This is accomplished by Mudra and Bandha
Mudras, in the context of Hatha Yoga, are those practices designed to pump up the energy in the body (now suitably purified and conditioned for this increase in "voltage").
The development of siddhi, or paranormal capacities, is a hallmark of the Mudra practices.
Most Mudras are a combination of physical and mental effort, ie. assuming a particular asana and then visualizing a certain activation or flow of energy within the body.
Bandhas are sustained muscular contractions which either contain or stimulate the flow of energy in the body. While there are only a few formal Bandhas, they are often combined with other techniques, such as Asana, Pranayama, and Mudra.
Fifth, cultivate mental focus and stillness. This is accomplished by various meditation techniques, including Laya & Mantra
It's important to remember that the final stages of practice in
Hatha Yoga is more of a meditative process. The Asanas, Pranayamas, Bandhas, and all the rest are all preparatory phases, meant to purify and energize the body and mind.
At this point, the techniques for meditation vary per text - for example, Gheranda Samhita lists several visualizations to meditate upon, but Hatha Yoga Pradipika prefers to focus on the inner sounds that arise with the awakening of Kundalini energy, and Siva Samhita focuses on the chakras as objects of meditation.
Hatha Yoga Pradipika even goes so far as to say that Hatha Yoga practitioners who don't also engage fully in meditation miss the point completely, and derive "no fruits for their efforts".
Remember, the fruit we're talking about here isn't better health or fitness, but a mind that rests in complete stillness!
Sixth, stabilize the quality of inner stillness. This is accomplished by entering and resting in Samadhi.
Samadhi...well, what to say? If it's a state where the mind ceases all movement, then it's not exactly an experience that is easy to talk about!
Inner stillness, at least the way the Yogis talk about it, is quite a bit different from simply feeling more relaxed, peaceful, or centered after a good Yoga class!
But make no mistake, this is and always has been the goal of Hatha Yoga - and of every Yoga, for that matter.