translate English to German: For travel within big cities, the easiest thing to do is to pick up a rechargeable contactless smart card like Suica/Pasmo (in the Tokyo / Kanto area) or ICOCA/PiTaPa (in the Kansai area), which will calculate the correct fares for you automatically. Note that the Suica/Pasmo cards can sometimes be used at places surprisingly far from Tokyo, and also in buses; though it can also happen that having entered the system with the card, you find yourself exiting at a point on a private railway where the card doesn't work, and you will have to pay cash for the whole journey, getting a receipt with which you can get your card cleaned up at a ticket office the next time you want to use it.
An kleinen Bahnhöfen (oder U-Bahn-Stationen) wird es schwieriger, hier muss man seine Fahrkarte an einem Automaten kaufen, der meist nur eine japanische Anleitung hat.