Hi aniina,
Thanks for the post. The hobby flying scene in India is dismal to non-existent. The flying school in Pune is non-functional for some time now so you will have to relocate for your hobby.
Here is a plan:
1. Find an existent school
2. Get your Class-III medicals done from any doc who is accredited to the DGCA, India.
Directorate General of Civil AviationIf you flunk that, sorry, flying is not for you.
3. Get a Students Pilot License (SPL) from the Chief Flying Instr (CFI -lots of acronyms in aviation, better get used to them

)
www.dgca.nic.in/cars/D7B-B2.pdf
4. Be prep to shell out upward of Rs 5000/- per hour for flying a single engine propeller aircraft in the Cessna 152 class.
5. SPL + 60 hours= PrivatePL(PPL) + 140 hours=CommercialPL(CPL) + 750 hours (approx) = AirlineTP(ALTP)
6. As a career, it is without parallel. The investment rounds out to about 20-21 lacs(with type endorsement on multiengines)
7. Check out
FAA - Home, the US Govt site. It is fab and lots of free downloads too, superb manuals in pdf, tonnes of stuff. Also
FlightSim.Com to get an idea about what you are about to get into