You need to learn Hindi to communicate effectively in India as speaking Tamil only is not enough to communicate. Foreigners and natives alike use Hindu as a common language in offices, business, temples and in the streets. You can learn Hindi through Tamil informally by enrolling through online courses and conversing with natives or formally by enrolling in a college.
Plan a long-term course to assimilate Hindi proficiently once you start a course. Look for a native speaker who knows Tamil online and learn the differences in sentence structures between the two languages from the person by listening to the words and sentence construction as a conversation is going on. Take note that Tamil sometimes uses the object -- subject -- verb in the sentence construction while Hindi uses the subject- object -verb.
Note the similarities: Tamil also has a subject -- object -- verb approach in the language set up. Compare the Hindi and Tamil alphabets, take time and learn it as a long-term course ensuring you know how to write it at the same time. Enrol to use library services where you can access both Tamil and Hindu books. Get a Tamil--Hindi dictionary and Hindi--Tamil dictionary from a Hindu Learning Center.
Read about the differences in applications of the pronouns, verbs and adjectives between the two languages while laying more emphasis on the Hindu language using a Hindi beginners hand book. Speak Tamil by comparing words constantly, translate sentences from Tamil to Hindi and vice versa.
Buy Indian movies, shows and documentaries and watch the programs subtitles in the Tamil language to help you understand Hindi conversation layout, events and the use of various words. Check if you can easily notice the differences by identifying familiar words from the books. Repeat sentences in the movies to analyse your proficiency and confidence in the language use.
Read advanced Hindi language and writing, practice the common phrases used in the streets, look for a friend from a Hindu Students Council of a college or Hindu temples and politely engage them in conversations in Hindi. Let them decide if you are fluent enough in the language without asking them about it, this helps you build more confidence and satisfaction of successful command of Hindu.
Interact with more Hindi speakers by visiting Hindu neighbourhoods, stores, colleges and as many social centres as possible and engage them in conversation; this will help you polish your speech, recognise the culture and understand the meanings even when spoken in different dialects and tones.