Hi G*,
As others have said, you can get SUICA or a JR pass, or use cash. Which is best for you will depend on what you plan to do. A JR pass allows you to use all JR trains including the Narita Express and I think the Nagoya equivalent, but I haven't flown through Nagoya so can't guarantee that! This includes the Hikari and Kodama bullet trains but as stated above it excludes the Nozomi, which is the fastest bullet train.
If you want to use a JR pass, it MUST be purchased outside Japan -
About JAPAN RAIL PASS is the official website.
JRpass.com seems to be linked to a UK company but they claim to deliver to Australia as well. I have never used this company before - indeed I hadn't seen the website before but it looks to have some useful info on it.
I have used
Welcome to Rail Plus - Rail Plus Australia and
JTB Australia - Travelling to Japan for bookings in the past without problems. Prices are in Japanese yen so sometimes you will get a better exchange rate at one place than another.
If you decide to use a SUICA, these can be purchased in Japan.
If you don't use any passes, you can buy tickets at any station. For subways and local trains you need to buy a ticket before you can access the platform - there are automated ticket gates to get into the station. The price depends on the destination. If you don't know where you are going or can't work out the price, buy the cheapest ticket and then when you arrive at your destination take your ticket to the office at the exit to the station and pay the difference. Sometimes there are machines to do this but from memory they are mostly Japanese-only without English options.
To book reserved seats using your JR pass and to purchase single-journey tickets eg Tokyo-Kyoto or Kyoto-Nagoya, go to the "Midori-no-mado-guchi" ("green window") at most large JR stations. This is the ticket counter and they can help you out. Sometimes this may involve charades or broken English but you should be fine in the larger areas such as Tokyo/Kyoto/Nagoya.
If you really only plan to go Tokyo-Kyoto-Nagoya I think price-wise separate tickets instead of a pass will be the cheaper option. A JR pass is not the most useful or cost-effective way of getting around Kyoto and Tokyo cities, although if you buy one you certainly can find ways to use it for sightseeing.
Have a great time and let us know if there are any more questions.
PS why are you flying out through Nagoya? KIX (Kansai Intl) is the more convenient airport for Kyoto and Osaka...