Public transportation in Japan is highly efficient, and very consumer-friendly, as everything in the Japanese society. Despite the system being very easy to use, some points need to be explained, as the public transportation system in Japan is one of the largest webs.
One of the first points that needs to be explained is that throughout Japan, all transportation signs are written both in Japanese and in the Latin alphabet, making it very easy even for us to get around. However, Japan does not have a government-run company that incorporates all the systems, instead, various companies compete to provide services. Whilst this can be very confusing in the larger cities (for example, Tokyo), it also helps to keep the prices low, as opposed to the countryside where only the Japan Rail (JR) runs.
Urban transport (buses, metros, trams)
The JR provides a service to the entirety of Japan, covering miles and miles of railways, although private lines also exist in every city. To answer the question directly: yes, trains are absolutely packed in the morning, to the point that it is necessary to have people push the customers inside the train. Luckily, the Japanese are small enough that you will not feel claustrophobic. This is also partly due to the fact that people enter the train and remain by the doors, instead of moving back. It is also recommended to remove any scarves or coats beforehand, as any journey of more than ten minutes will make anyone sweat.
Overall, the system remains the same regardless of the company.
In metros or suburban trains, you should purchase a ticket based on how far you wish to go (you can find the station on the maps at the entrance of the station, although sometimes they are only written in Japanese) and insert it in the gates before passing through. Gates in Japan are generally open to let the crowd through at peak hours, and close if something is wrong. They are not particularly reactive though, so it is possible that they will close behind you or on one of your legs. It is expected of you to turn back, collect your ticket to go present it to the man at the booth (although no one will chase after you if you don't). You should always collect your ticket, as you will need it to get out.
If you decide to change your destination at some point during your journey, fare adjustment machines are located at each exit (or talk to the man in the booth again – or gesticulate, present your ticket, and grunt the name of the station you want); you will then be able to pay the difference or have it reimbursed. Tickets are automatically eaten by the machines as you leave, to prevent waste.
Should your journey cover a transfer which includes a change of companies, you must buy a “transfer ticket” rather than paying the full price on the one company, as the machine will eat your ticket and you will find yourself talking to the booth man again, this time to explain that you were tricked out of your money.
You might want to watch out for the destination of your train, or which category it is (local, semi-express, express) as you might otherwise miss your stop. Luckily, it is always clearly indicated.
Buses work pretty much the same, although not all charge on distance (for example, if the route is short enough that they consider it to be one fare only). You should enter the bus, tell the driver which stop you plan to get off at, pay the required amount and take a seat. These buses give change back, and you can even pay with bills (usually inserting a 1,000 bill makes your purse inflate with all the change). Call for your stop.
In some cities, the buses work on a ticket system. When you enter the bus, the driver asks you to take a ticket with a number printed on it. A board at the front of the bus indicates the price from every location (or number) thus indicating how much you should pay when you get off. Unfortunately, these buses require exact change.
Often, buses are much harder to work out as the routes are hardly explained on the bus stops, or in the buses themselves. Also, the stop names are not directly relevant to their location. Overall, I would suggest taking buses only if someone has told you the exact route (and even then they can still be confusing between platform number and bus number). In Japan, it is not customary to say hello to the bus driver, and they will always look entirely surprised if you do.
Bus drivers announce the stops, but also a number of interesting things such as what he is doing, be it slowing down, speeding up or turning. Supposedly, this is so that elderly passengers are prepared for the bus movements.
Trams are fewer in Japan, but not unheard of. The ticketing system is different again, as this time you enter through the back and must exit through the front, where the driver sits, where you pay your fare. This is particularly handy if you are travelling with a large suitcase or a large amount of grocery bags. Mind you, if you say sumimasen loud enough, people will move to let you pass.
Cost (student, pensions, passes) and reliability
Travelling within a city is not entirely exorbitant, as long as you stay within the centre itself. As mentioned above, prices are counted on the length of the journey, although many different kinds of passes exist. Express trains are more expensive, as you pay the basic fare for the distance covered and then a surcharge based on how fast the train is (this explains the different prices available for different types of shinkansen, of which the nozomi is the most expensive, but also the fastest). Overall, the express trains are very expensive in Japan.
Because all the companies are different, it is very difficult to find passes in Japan – you should therefore ask at your relevant station. However, there are still a few options (detailed below).
In Tokyo, it is possible to use PASMO commuter tickets, which are set from one point to another and allow you to get off at any station located on this route. For a monthly pass, it is more or less equal to 60% of the cost of individual tickets, and allows for greater movement. PASMO tickets can also be used as rechargeable IC cards, allowing you to top-up the card and travel anywhere on the network without buying individual tickets every time. The SUICA card is nearly identical, but does not provide the commuter ticket option, although it has the advantage of being usable in all big metropolis in Japan. These two IC cards can also be used in various outlets in Tokyo, in order to pay for newspapers, food or drinks from dispensers.
As a student, you must show your student card and a special card given by your university, to be stamped every time you buy a new commuter pass. This card entitles you to important discounts on your commuter pass, the rest being paid by your university.
The Japanese public transport is highly and completely reliable. Not only do they run punctually approximately 99% of the time, they are also comfortable and clean, providing seat heating in the winter and air conditioning in the summer. The only occasions when trains are for big incidents such as suicides, landslides or earthquakes. Sadly, suicides are quite frequent in Japan, but the Japanese have become to accustomed that trains run at most half an hour late in these cases. In case of massive earthquakes, the lines are reconnected as quickly as possible, although the bullet train (shinkansen) gets priority. This means that local trains might not leave for some six hours.
City buses are slightly less reliable, but the Japanese are raised to be punctual, and so it is possible to see buses run past before their actual time. Overall, make sure you arrive plenty in advance.
National transport (planes, coaches, trains)
As Japan is a country of islands, trains are not always the best option to move around. Planes are not only much faster (the main island is very long and travelling all the way across in shinkansen can be very expensive), but they can also reach destinations that would otherwise be blocked off. As such, many planes fly all across Japan every day, with companies such as ANA, JAL, Skymark, Skynet, Air Do and Starflyer.
Coaches also run across Japan, but are usually not recommended. Although entirely safe, the journeys are either long or tedious and just as costly as the train. They do have the advantage of offering routes otherwise not available but there is no information in English so be prepared to use your Japanese. Coach trips are often included in set tours, and can be a useful way of travelling if you have little time.
The Japanese trains run not only very fast but also very frequently. Different kinds of shinkansen run approximately every six minutes at peak times, although in some regions there might only be one a day. The bullet trains are entirely functional, provide a lot of space but look completely bland (unless if you can see the newest nozomi, with its beak-shaped engine) and their ticket includes any transfer you have within the JR in any city.
You can buy tickets for the shinkansen yourself at some machines, but it is highly recommended to go to a booth where you can talk to someone, as there are so many options available and there is no English offered on these machines. You probably won't find someone who speaks English either, but the hassle is worth it just for the sight of the agents working their machines at lightning speed. Shinkansen tickets can be exchanged up to the hour at which your train leaves.