Yoga is a link to connect the souls (one's Atma) to God, the Super Soul (Parmatma). Yoga is a process by which the adult (Purusha) gives up evil qualities ie. Kaam, Krodha, Lobha, Moh & Ahankara to create a real connection with God.

Maharishi Patanjali, the founder of yoga described yoga as "Yogash Chitta Vritti Nirodha", ie. Yoga makes the mind focus on its soul. Yoga as a word or "shabd" occurs frequently in the ancient text, the Shastras, Upnishads and the Sutras. It is often used in a variety of context and with different meanings whose sanskrit equivalent could be any of sambandha, sannahara, upaya, sangati, jnanana or Yukti.

Gita says that equanimity must be maintained through joy or misery in one's life. Modern life is indeed in need of that equanimity which comes from yoga. So lets focus on the parts of Astanga yoga by Maharishi Patanjali in order to get peace, happiness & health by practising it regularly.

Astanga (Eight-faceted) Yoga by Maharishi Patanjali
Yoga is known as astanga or eight faceted yoga & these eight facets are enumerated as under -
1. Yama (Yama Stands for Ahimsa. Patanjali said, "Ahimsa Pratishtayam Kriya Phalasrayatam". Speak truth & think truthfully)
2. Niyama (Niyama encompasses the five concepts ie. Soucha (cleanliness), Santosha (contentment), Tapas (penance), Swadhyaya (Self realisation) & Ishwari Pranidhana.
3. Asana ("Asanam Pran Samrodha: Pratyahara Scha Dharanam Dhyanam Samadhiretani Shadangani Prakirtita" - Asana helps to condition the body, mind and soul.)
4. Pranayam (Regulation of "Prana" is called Pranayam)
5. Pratyahar (Pratyahar teaches us how to control our Indriyas)
6. Dharana (Dharana means concentrating one's mind on either a center of the brain or on a devotee of God or on the almighty himself.)
7. Dhyana (The word Dhyan is derived from Dhaichintay, which means to think deeply about a thing or subject.)
8. Samadhi (Samadhi is combining Aatma (one's soul) with that of Parmatma (the supreme soul))

Both Yoga & Ayurveda cautions one to stay away from suffering. This may be gleaned from our scriptures. One of which is given here -

Yoge Mokshe Cha Sarvesham Vedananmavartanam Moksho Nivritti Vischeshya Yogo Moksha Pravartaka

{Charak Shareera, 1:137}

Yoga can bring about personality changes (Chitta Vritti Nirodha). The mind (Manas) and speech is brought under control. Then, with focus (Dhyaana) one can rid one's mind of negative qualities such as 'ahamkara, kama, krodha & parigraha'. This achievement is the beginning of fusion with the Brahma and so salvation (Mukti).

Yoga & Ayurveda are one in the belief that the health of the individual is all important. One shloka from the scriptures defines this statement very well -

Dhoutirvastistatheneti Navliki Tratakam Tathaa Kapaala Bhati Schaitani Shat karmani Samaacharet.

{Ghoranda 1/12}

As adopted in ayurveda, the Sat Karmas reduce the state of diseases in the body and pacify the Rajas & Tamas. As adopted in Yoga, the Sat Karmas purify the Sharira (body) & the Manas (mind). Yoga and Ayurveda are one in belief - both practices are aimed at achieving a state of (Prasannata) ie. peace in an individual.

So it is very much clear that the wholesole objective of Ayurveda & Yoga is to give man health, peace, contentment, thereby leading a happy & prosperous life and enjoying the journey of life in divine & with divine, hand in hand.