Public transportation in Japan is leagues ahead of America in all areas. The main methods of transport are buses, subways, JR trains, bullet trains, and ferries. For all of these services, Japan offers prepaid IC (integrated circuit) cards that can be used to pay the fares by simply “tapping on” when entering and “tapping off” when exiting. These IC cards can be “topped off” (refilled) at machines located outside the ticket gates. While each area of Japan has a different corresponding IC card, nowadays you can use any IC card in any area.
If you are a tourist in Japan, you can purchase a special rail pass that provides you with unlimited rides on JR train lines, bullet trains, and a few other special modes of transfer within a certain period of time. The price of the rail pass may seem a little high at first, but when you take into account the price of the bullet trains normally (~$50-$100 one way), it is well worth the cost.
Buses
The buses in Japan, while useful, often suffered from the same problems in America. On one hand, the buses were more timely than in America. On the other, the routes were confusing, the times infrequent, and the prices high. I often had to use Google Maps to find the closest and soonest bus, since the schedule/map was too difficult to use on the spot. For daily, routine routes, they are more helpful.
Subway
The most useful form of city transport in my opinion. The subways were frequent, fast, and timely, with useful routes to all the main sights of the city. The price for the subway was a bit high, but the convenience was well worth it.
JR Trains
These are similar to Amtrak trains in the US as they connect the big cities of Japan with smaller towns and other big cities. They were useful for getting to places that were out of range of the subway system. The times are pretty frequent for local trains, with rapid express trains being somewhat infrequent. During rush hour, if you don’t have a reserved seat, it can become a little uncomfortable since the unreserved cars have subway-style seating.
Bullet Trains
The most amazing form of transport I have ever used in my life. I (and most Japanese people) loved the shinkansens (bullet trains). They are insanely timely, veeeeery fast, very comfortable to ride on, and very frequent. These trains make sightseeing around Japan so easy since they connect nearly all major cities in Japan. Unlike airplanes, there is a lot of legroom, no need to worry about luggage sizes or security, and great sites from the window. You can reserve seats in advance or simply hop onto a non-reserved car (if you have the rail pass).