For Doing Naval Architecture from Indian Maritime University or colleges affiliated to Indian Maritime University, Chennai . You first need to give Indian Maritime University common entrance test (IMU-CET) which is conducted once in a year for engineering department. After clearing that exam you have to go for the counselling process depending upon the rank in IMU  CET you'll get the college. You can check imu.edu.in  for further details.

For affiliated colleges you have to separately apply on their websites but for that you also have to clear IMU-CET first . Different affiliated institutes have different selection procedures.