Slowing down the breath ,
Increasing exhalation:inhation to 2:1 when not exerting yourself,
Letting go of thoughts, being a witness to your thoughts, silencing that voice in the head,
Relaxing, letting go, un-tensing all muscles,
All of this is Yoga, and all of this is a pre-requisite to Yoga.
Keeping the mind in a non agitated state, by giving up negative attitudes like envy, lust and greed, and cultivating positive attitudes like compassion, love, and forgiveness is Yoga. This is not something you can ever be perfect in, it should rather be seen as the direction in which one should take the mind.
The above is not something you just "do" and forget about, it is something you do to integrate into your life, that is Yoga.
Putting the body in certain positions, asanas, that increase the flow of Prana, vital energy, in a constant state of relaxation ( except the specific muscles being tensed in the pose) , is Hatha Yoga, which people refer to as Yoga nowadays.
People divorce the practice of asana from the mind and the beareth, and don't bother about the pre-requisites. In that case, it merely becomes another form of physical exercise , not without benefit, but it will not enable the practitioner to progress further.
Asana is merely the third step in the eight step Ashtanga Yoga outlined by Patanjali. Its side effect is good health and vitality but that is not the goal.
Any person of any age can do Yoga.
The goal of Yoga is much loftier than mere attainment of bodily health, which is an almost guaranteed outcome of regular asana practice. The goal of Yoga is to attain union of the individual consciousness with the cosmic consciousness, and asanas are practised to make the body ready for more advanced practices.
Once the body has been rendered free of ailments, and has been made flexible and pliant with asana practise, is when one goes to the next step, Pranayama. In case one jumps into advanced Pranayama practice without laying the foundations, it may result in more harm than good. Basic breathing exercises are fine, but advanced practices are ruled out. Most of us do not even know how to breathe, and we talk of Pranayama, it is necessary for most people nowadays to attend classes to learn how to breathe.
Where the breath goes, energy follows. The practice of Pranayama is actually the practice of "yama, control" of the "prana, energy" , which is the vital energy that flows through our nadis, invisible channels or pathways that carry energy through the body.
That takes care of the Annamaya Kosha and the Pranamaya Kosha, the Gross Body sheath and the next higher sheath of the Energy Body.
Yama, Niyama, Asana, Pranayama, are the first four steps of the eight steps of Patanjali, and it is Bahiranga Yoga, the outwardly focused Yoga
Then starts Antaranga Yoga, Internally focused Yoga, the process of bringing the mind under control. Meditation is not truly possible unless one puts the gross body and energy body in a state to be ready for it. Meditation is also not possible unless one learns to be truly, truly, relaxed.
For a person who is truly relaxed, ideas and inspiration strike the mind effortlessly, said Cicero, the ancient Roman philosopher. Relaxation is essential for true well being.
Antaranga Yoga has four steps, starting with Pratyahara, withdrawal of the mind from sense objects.
Then follows Dharana, concentration , where the mind is steadily focused on one single thought, to the exclusion of all else, just like oil poured from one jug to another, flows in a continuous stream. It is almost impossible for the mind to be brought under such control even for a few minutes, and the meditation practices are all aimed at focusing the mind on a single thought.
From "single thought" to thoughtlessness or meditation, or silence, is a process that automatically has to happen, just like sleep automatically happens, you can never "do" sleep. Dhyan is the seventh step of Patanjali's eight steps.
Then comes Samadhi , union with the Supreme, a state which is difficult to reach. A few in every age, the Sages, manage to reach such a state. Patanjali even goes on to describe different types of Samadhi!
The above is the path of Raja Yoga. The Gita mentions other Yogas as well, which can serve equally well for attaining the same state of Union. They are Karma Yoga, Bhakti Yoga, and Jnana Yoga. Depending on individual temperament, it is for us to choose which path to take.
The paths are not mutually exclusive. Working without worrying about the results as in Karma yoga, having an attitude of Bhakti as in Bhakti Yoga, and sifting the real from the unreal as in Jnana Yoga, are all necessary things to do, to a greater or lesser degree.
As the Masters have stated, the aim is the Mountaintop, and many paths lead to the same place. Once you reach the top it does not matter which path you took.
Reaching the top of the Mountain is Yoga, and travelling up any of the paths is also Yoga. Union of the body, mind and spirit is Yoga.