Method of payment
One of the biggest things in Japan is that you cannot use your country's banknotes. Currency of Japan is Yen(JPY) and there is almost no where in Japan accepting other currencies such as USD or EUR except in US military bases.
Therefore you have to exchange to JPY before departure or exchange at arrival in Japan. Exchanging at airport is very simple and easy but not so easy in cities.
Banks are everywhere but not all of them are able to exchange from foreign currencies. Then, there are more bureau de change in large cities than before, but definitely you should bring substantial amount of JPY before arriving in Japan.
How much should I bring?
Of course it depends on the duration of your stay in Japan but I recommend to have at least JPY 2000 per day. Which means if you stay 10 days, better to have at least JPY 20000 in your wallet or in purse.
Can I pay by credit card?
Yes, except if you stay at extremely cheap place.
At ticket office only.
From above, you will need cash for paying the admissions and tickets.
Suica & PASMO
If you do not want to carry high amount of cash, or do not want to spend a time buying ticket each time at metro station, strongly advise to get SUICA or PASMO, a contactless smart card which is able to recharge.
Suica is by JR East railway and PASMO is by other major railway operators in Tokyo, and if you have one of them, it can be used at other railway operators in other big cities, such as Osaka and Nagoya. Suica and PASMO can be used on local buses in Tokyo too.
Then, if you have Suica or PASMO and there are substantial amount in it, you can ride trains and subways in Tokyo without buying a ticket. What you have to do is that touch the ticket gate for contactless smart card usually mentioned as IC with Suica or PASMO. You can save your time at station and also fare is slightly cheaper than ordinary paper ticket.
Also Suica can be used at stores or cafes which accept electronic payment system. Sometimes the facility accepts Suica but not the credit card.
JPY has 4 bills. 10000, 5000, 2000 and 1000. 2000 is very rare now and hardly accepted at ticket and vending machines.
Vending machines and local buses accept only 1000 note. Therefore you should always have at least a single 1000 yen or certain amount of coins.
There are 500, 100, 50, 10, 5 and 1 yen coins. 5 and 1 yen coins cannot be used at ticket machine or vending machine.
I recommend to carry a wallet/purse and a coin purse or pouch during your stay in Japan. Carry your credit card and large denomination bill(10000 and 5000 yen bills) inside the wallet and place your Suica/PASMO, coins and a few 1000 yen bills inside the coin purse. The wallet/purse can be kept inside your bag where not easy to take it out and keep the coin purse/pouch inside your pant's pocket or bag's pocket where easy to take out.