There‘s Suica and Pasmo and some other IC cards that give you access to the homogenous and highly efficient and punctual public railway and metro system of Japan.
The cards are simple: you can buy them at a station, precharged with 500 yen (around 5 USD). You use them when you enter and leave stations. The fare is calculated automatically and charged from your deposit. You can top up your balance easily with cash at every station.
A Suica card
Leaving a metro station, the fare for the trip is shown above, below the balance of your card
Machines to charge your IC card
In case you don‘t speak and read Japanese...
Charge IC card
Enter IC card, chose amout to top up, insert the bills