TL;DR
Articles 14 to 18 of the Constitution give you the right to equality. The State cannot discriminate against you on grounds of religion, race, caste, sex, or place of birth. You are equal before the law. There are some exceptions (e.g. special provisions for women, children, or backward classes) that the Constitution allows to achieve real equality.
Article 14 — Equality before law
Every person is equal before the law. The State cannot treat two people differently if they are in the same situation, unless there is a good reason. This is called “rule of law.” It applies to the government and to the courts.
Article 15 — No discrimination
The State cannot discriminate against any citizen only on the grounds of religion, race, caste, sex, or place of birth. You cannot be denied access to shops, public places, or government services on these grounds. The State can make special provisions for women, children, and socially and educationally backward classes (e.g. reservation) to promote equality.
Article 16 — Equality in public employment
All citizens have an equal right to be considered for government jobs. No one can be denied a job only because of religion, race, caste, sex, or place of birth. Again, the State can reserve posts for backward classes if needed to achieve equality.
Article 17 — Untouchability abolished
Untouchability is forbidden. No one can practise it. Any such practice is an offence under the law.
Article 18 — No titles
The State cannot give titles (like Sir, Rai Bahadur) except for academic or military honours. This supports the idea of equality: we do not have a class of people with special titles.
Source: Constitution of India, Part III. For full text see India Code (indiacode.nic.in). Related: Right Against Exploitation (Articles 23–24), Constitution and Equality.