We strongly recommend you to purchase an IC card ‘manaca’. It can be used for almost all the public transportations including Meitetsu train, JR train, Nagoya Municipal Subway and Bus. This card can also be used for public transportation in Tokyo.
When the manaca is no longer needed, the card can be exchanged for the deposit (500 yen) at any ticket counter.
If you want to take a first class car for traveling Centrair to Kanayama (or return way), you need to purchase a μTicket (360 yen) along with a railway ticket/manaca. You can purchase a μTicket at the ticket counter and the ticket vending machine.
For more information
Meitetsu ticketing : http://www.meitetsu.co.jp/eng/ticket-info/purchase.html
Nagoya Municipal Subway : http://www.kotsu.city.nagoya.jp/english/english_sub.html
How to use manaca : http://www.meitetsu.co.jp/eng/ticket-info/manaca.html