From Nagoya Centrair Airport, we warmly suggest you to take the "µ-sky" limited express train going towards Nagoya Main Station (simply referred to as "Nagoya"). Here is the official link with all relevant information. You can choose between non-reserved (850 yen) and reserved seats (1,200 yen). All signs, directions, and announcements are in English language too - you shouldn't encounter any problem.
If you are thinking of continuing your journey by taxi, you'd better get off at the stop "Nagoya", which is Nagoya central train station.
If you think of using public transport, you'd better get off at the stop "Kanayama". Click here for further information.