Common Answers
Some of the more simplistic answers to this question include: Anyone born in India is automatically a Hindu (the ethnicity fallacy), if your parents are Hindu, then you are Hindu (the familial argument), if you are born into a certain caste, then you are Hindu (the genetic inheritance model), if you believe in reincarnation, then you are Hindu (forgetting that many non-Hindu religions share at least some of the beliefs of Hinduism), if you practice any religion originating from India, then you are a Hindu (the national origin fallacy).

The Real Answer
The real answer to this question has already been conclusively answered by the ancient sages of Hinduism, and is actually much simpler to ascertain than we would guess. The two primary factors that distinguish the individual uniqueness of the great world religious traditions are
a) the scriptural authority upon which the tradition is based, and
b) the fundamental religious tenet(s) that it espouses.
If we ask the question what is a Jew?, for example, the answer is: someone who accepts the Torah as their scriptural guide and believes in the monotheistic concept of God espoused in these scriptures. What is a Christian? - a person who accepts the Gospels as their scriptural guide and believes that Jesus is the incarnate God who died for their sins. What is a Muslim? - someone who accepts the Qur'an as their scriptural guide, and believes that there is no God but Allah, and that Mohammed is his prophet.