Andaman & Nicobar can be reached via water and Air only. The place has Veer Savarkar International Airport in Port Blair. You can take flights from Kolkata and Chennai to reach Port Blair.
If you don't want to go via flight, you can travel by sea. Ships to Andaman & Nicobar go from Chennai, Vizag or Kolkata. It usually takes 60-70 hours to reach Andaman & Nicobar.
There are auto-rickshaws and taxis available in Port Blair. You can take hire any to visit nearby places. Buses also run from one place to other.