Hindu is not a Vedic word, and it is said that the word was perhaps coined by the Persians. They could not pronounce the word Sindhu so they called the people living in the Indus Valley, Hindus. We therefore do not find the word Hindu in the ancient scriptures, though in the recent works we do find the word being explained as him apasabdam dyati khandayati iti hinduh हिं अप्शब्दम् द्यति खण्डयति इति हिन्दुः, one who condemns falsehood, also meaning one who is committed to the truth is a Hindu. Hinam dasyati iti hinduh हीनं दुष्यति इति हिन्दुः, one who condemns anything that is low, base or wild can also be called a Hindu. Further, the Vedic culture is primarily based on worshipping the gods. Narayanadi-devatd bhaktah नारायण-आदि देवता भक्त, one who is the worshipper of gods such as Narayana can be called a Hindu. Thus different explanations are given for the word Hindu.
Hence we may say that one who follows the eternal fundamental values of life, one in whose life the worship of gods, is very important, one who lives a responsible life, one who is committed to a righteous way of life, one for whom the spiritual growth is very important in life and hence one for whom matter subserves the spirit, can be called a Hindu.
A Hindu is also the one who has faith, and trust in the Vedas. What we call Hinduism can properly be called vaidika-dharma. Hindus follow the teaching of the Vedas and many other texts that are derived from the Vedas. The Vedas are the fundamental texts, then there are the smritis, the puranas and also a whole body of literature based on the Vedas. The followers of the teaching of these texts can be called Hindus. Thus, Hinduism is a religious way of life based on the vision of life provided by the Vedas.
Hinduism is very broad-minded and inclusive. It does not matter, which tradition, place and time you hail from. As long as you follow the fundamental principles of the Vedas, have the right perceptions in life, follow the right values, you are a Hindu, and are qualified to attain moksa मोक्ष, which is the end Hinduism aspires to attain. Hence, we can say that one born a Hindu. There are no rituals or ceremony need through to become one. Hindus, in fact, do not see a need to preach conversion.
As best as I know there is no formal process of conversion. Hindus never converted others, but anyone wanting to practice Hinduism was included in the fold. Therefore Hinduism spread far and wide beyond the borders of India to China, Java, Sumatra and other places. It is by willing acceptance, and not conversion that one becomes a Hindu.
Swami Viditatmananda Saraswati