How do I actually exercise these rights?

You approach the Data Fiduciary first, using the means it has published for this purpose. Every Data Fiduciary must publish the contact details of a Data Protection Officer or another person able to answer questions about processing. If you are not satisfied with the response, or receive none, you may then complain to the Data Protection Board of India. The Act expects individuals to exhaust the Fiduciary's own grievance mechanism before escalating.