The closest airports are Likabali and Tezpur however connectivity is erratic. It's best to fly to Guwahati (450 kms from Ziro) and proceed from there.
The closest railhead is Naharlagun (about 3 hours away from Ziro). There are overnight trains to Naharlagun from Guwahati.
Ziro is 450 kms from Guwahati (Assam), about 12 hours by road depending on the weather. There are two main entry points to Arunachal Pradesh - Bandardewa Gate and Kimin Gate. (Note: All non-residents need an Inner Line Permit to enter Arunachal Pradesh. Foreigners need a Protect Area Permit)