Essential study materials for understanding Indian polity for UPSC include the Indian Constitution, NCERT textbooks, and standard reference books like "Introduction to the Constitution of India" by D.D. Basu. Aspirants should also refer to the latest publications on polity, government schemes, and current affairs to stay updated. Reviewing and understanding judicial pronouncements and constitutional amendments is crucial. Additionally, following reputable news sources can help contextualize political developments and government policies, providing a holistic understanding necessary for answering polity-related questions.