It is a long journey from class 12 to NASA but if there is a determination and strong will to work hard in that direction, it is very much possible. It is good that you have a liking and interest in a specific area that of Astrophysics and you want to excel in it. Having a dream is a good thing and doing all out efforts to achieve it is still a better thing.
To realise your goal you must apply and get admission in B.Sc. Astrophysics course. This is a 3 years course and students who has completed 10+2 with Physics, Chemistry and Mathematics and having at least 50% aggregate marks are eligible to apply for this course. The written test is conducted by the institution or the university where you want to take admission followed by an interview cum counselling session. During this course you will learn how the natural phenomenon occur in the universe and what is its composition and constituents. You will be studying subjects like Thermodynamics, Electromagnetism, Classical Mechanics, Waves, Optics, Modern Physics, Atomic, Nuclear and Quantum Physics, Solid State Physics, Relativity, Quantum Physics, Fluid Mechanics, Latest advancements in Astrophysics etc.
Some of the good institutions / Universities for B.Sc. Astrophysics course are Osmania University, Hyderabad; College of Science & Technology, Andhra University, Visakhapatnam; Madras University, Chennai and Punjabi University, Punjab.
After completing the B.Sc. course one has to pursue M.Sc. in Astrophysics for which again one has to appear in written test for M.Sc. Astrophysics and pursue this 2 years course. One should have at least 50% aggregate marks in B.Sc. Astrophysics or B.Sc. in Physics, Mathematics and Chemistry. So students who have missed admission in B.Sc. Astrophysics can again join this stream after doing normal B.Sc.
M.Sc. Astrophysics is an exhaustive course and covers advanced aspects related the universe like Applied Mathematics, Analog Electronics, Classical Mechanics, Positional Astronomy, Digital Electronics, Quantum Mechanics, Celestial and Fluid Mechanics, Space Physics, Astronomical Techniques, Stellar Atmosphere, Electromagnetic Waves & Radiating Systems, Advanced Electronics, Galactic System & Cosmology, Stellar Structure & Evolution, Plasma physics, Lasers and applications etc.
Some of the good institutions for M.Sc. Astrophysics are Indian Institute of Astrophysics, Bangalore; Osmania University, Hyderabad; BITS Pilani, Rajasthan; Andhra University, Visakhapatnam and Punjabi University, Punjab.
After completing M.Sc. in Astrophysics, it is time to apply in some foreign institution for MS in Astrophysics and specialisation in one of the constituents or apply directly for research work. At this stage one has to apply for GRE which facilitates for admission in foreign universities. If one is not able to get a seat in foreign institutions then there are research avenues in India itself and one can apply for admission in them for pursuing PhD. Some of the institutions where this can be pursued are Indian Institute of Astrophysics, Bangalore; Indian Institute of Space Science and Technology, Thiruvananthapuram and Aryabhatta Research Institute of Observational Sciences, Nainital.
Once a person gets good knowledge in this field and is engaged in research work then he can send his resume through the institution for his willingness and desire to work in NASA in any project which is given to him as per the knowledge and experience. NASA recruits people from all over the world in its research work and many Indians have made their place there. One can even try to get fellowship for research work abroad from where again he may get opportunity to get assignment in NASA.
Please remember that space and universe science is a very big field and a person will remain a research scholar or scientist throughout his career. So those who are having interest in Astrophysics can definitely pursue this career.
Knowledge is power.