If you are commuting to work or to school, you can get what`s called a commuters pass (teikiken, 定期券). You can buy them at the station office or the ticket vending machines. You will be asked to fill in the name of the station that is closest to your house, as well as the name of the station that is closest to your work, pay a set amount and then you will be able to use the train going to and from those two stations as many times as you want for up to one, three or six months. Important to note here, is that you can get off anywhere you like in the middle, and it will still be free. Usually, these will be simply printed on the aforementioned IC-cards, but paper versions are available as well.
Public transport in Japan is widely available. Especially the train network is often praised as one of the most well-run and punctual in the world. In the larger metropolitan areas, many people rely entirely on trains to get to work, go shopping or whatever other transport needs might arise. With space being very limited, parking is often very expensive in city centres so many people commute by train. Train stations can be confusing at times since stations are usually not shared between train companies, so if multiple companies are servicing one area, there will be multiple train stations with similar-sounding names. Besides, many stations will have multiple ticket gates (kaisatsu, 改札), and even more exits.
Most people use so-called IC-cards (aishii kaado, IC-カード) when using public transport. These cards can be charged with money, and when you want to ride the train you simply touch the appropriate area at the ticket gate with your IC-card to go through. You do the same when exiting the station where you get off, and the appropriate sum will be taken from your card. If funds are insufficient an error message will appear, and the gates will not open. There are always charging points in the station, so simply top up your card and you will be able to exit. If you do not have the cash to charge your card, you might have to go all the way back to the station where you started and speak to a station attendant there. There are regional variants of IC-cards, but the two most common types, the PASMO and Suica cards can be used almost everywhere in the country. IC-cards can be bought at ticket vending machines in train stations, with Japan Rail (JR) stations selling the Suica card, and most other stations selling the PASMO card.
Busses and taxis are of course available as well. But busses are not as vital of a link in the mobility chains, being mainly used by elderly people, and are a lot less frequent than they might be in other countries. Taxis are convenient and offer a variety of payment options but can be expensive. One final option for getting around in Japan is of course the car. Requirements for being allowed to drive in Japan differ depending on the country you are from, so make sure to check the website of the Japan Automobile Federation.