Indians can visit Andaman without any restrictions. The easiest way to reach Andaman is by flight. Foreign nationals can avail permission from the Indian Missions Overseas, Foreigner's Registration Offices at Delhi, Chennai, Mumbai, Calcutta, and also from the immigration authorities at the  Delhi, Mumbai, Calcutta and Chennai airports. The initial permit is valid for 30 days and can extend it to another 15 days.
By Air- Private / Public: Direct flights are available to Andaman from Chennai, Bengaluru, and Kolkata. From most of the Indian airports, connecting flights are available to this destination. If you own a plane after taking permission from authorities, you can use your own plane to reach the island.
By ship- Passenger/ Cruise/ Sail Yacht: By making a prior booking through the government site, travelers can reach Andaman in a passenger ship from Vishakapattanam, Chennai and Kolkata.  Cruise ships make a halt at Andaman islands for a few days and you can plan the journey through a trustable travel agency.