From Nagoya Centrair Airport, we warmly suggest you to take the "µ-sky" limited express train going towards Nagoya Central Station (aka "Meitetsu Nagoya" or "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.
You can then continue your journey by taxi, which are relatively inexpensive and very efficient.
Otherwise, you can use our public transport: in this case, click here for further information.