After passing 12th, you can apply for the IMU CET exam for marine. Every year, IMU conducts a common exam for different type of marine courses like, marine engineering, naval architecture, DNS, nautical sciene. After clearing the exam you can apply for colleges, and after clearing some medical exams and interviews you're good to go. 

Hi,
To become Naval Architect, aspirants have to complete the graduation course in Naval Architecture also can do Marine Engineering.
In addition, they have to study the Master of Science in Engineering and the research program in Engineering and Applied Science for getting top designations in the Naval Academy.
The eligibility criterion to apply for the Bachelors course in Naval Architecture and Marine Engineering is the completion of the 12th examination from a certified Institute.
Aspirants should have studied the program in Science stream with Maths as a subject
Along with one must clear NATA  and entrance exam as per university.
Naval architecture programs at the bachelor's level are typically offered at coastal schools holding affiliations with the Navy,