The knowledge of Tamil alone will greatly hinder your chances of communication with people from parts of India other than Tamil Nadu and Pondicherry. As India's national language, Hindi enjoys the status of being widely spoken and well accepted in all parts of the country and by people of all linguistic derivations. While learning Hindi is not an easy task, once mastered, it will open new doors for communication and opportunities.
Commit to a long-term learning plan. Hindi is a difficult language to learn, and proficiency in it requires a committed and sustained long-term strategy that increases in usage and difficulty as time passes.
Familiarize yourself with the sentence structure. While Hindi and Tamil both utilize the Subject Object Verb structure, it is also not uncommon in Tamil to use the Object Subject Verb sentence structure. This is critical to distinguish.
Learn the Hindi alphabet. This should be one of the first steps of your long-term plan. Learning the alphabet and sentence structure will provide you with an opportunity to read and thereby learn more.
Learn the most frequently used words in Hindi. This will include pronouns, verbs and adjectives. A good list can be found with a quick search on the Internet or in a book that targets beginner Hindi learners. This will help in familiarizing you with the language.
Watch Hindi movies and TV shows. It will be helpful to have Tamil subtitles; by watching movies and TV shows you get the chance to identify vocabulary you have learned and put verbs and adjectives into context.
With the aid of Hindi-Tamil and Tamil-Hindi dictionaries, try to read and translate. Begin with vocabulary and elementary sentences and proceed further as your confidence and proficiency increase.
Practice spoken Hindi as much as possible. This can be done through repetition of lines in movies, songs and TV shows, through identification of objects or simply by reading aloud.
Utilize the Internet, which offers abundant resources on learning Hindi. This includes alphabet familiarization, vocabulary lists, speaking drills and advanced material.
Find a friend who speaks Hindi and practice with him as much as possible. Interactions are the best way to learn a new language.