Sanskrit, the language of the Vedas and Vedic thought, is one of world's oldest tongues. It is from Sanskrit that present-day Indian languages such as Hindi, Gujarati and Bengali were conceived. While Sanskrit is a difficult language to master, learning it through Hindi makes it easier, as both are written in the same alphabet (Devanagari).
Focus on learning vocabulary. While they are both written in the same alphabet, Sanskrit has a different vocabulary than Hindi. However, the ability to read the alphabet will help you learn new words and meanings in Sanskrit.
Start writing it, as that will help you recognize newly learned words and enable you to distinguish it from Hindi. Initially focus on writing new words and simple sentences. As your knowledge of the language grows, increase the difficulty level.
Learn the grammar. With the aid of beginner's guide to Sanskrit or a book on Sankrit grammar, familiarize yourself with syntax and grammatical nuances unique to Sanskrit. Your knowledge of Hindi will come in handy here.
Commit to reading a few pages of a Sanskrit to Hindi/Hindi to Sanskrit dictionary every week. This will enable you to learn new words, focus on grammar and put the language in perspective.
Read materials in Sanskrit. This can be done online or through the purchase of a book. Start at the elementary level and increase only when you make clear progress. Reading will help contextualize verbs, adjectives and other grammatical nuances.
Practice speaking it with someone who knows Sanskrit. Conversing in the language will support your learning experience and identify areas which need improvement.
