Greece has been part of the Eurozone since 2001 and the country's monetary unit is the Euro. The exchange rates of foreign currency may vary and money can be exchanged at a bank or official exchange shop where you will get the best running rates. Some hotel receptions exchange foreign currency, while USD as well as GBP is accepted by shops in tourist zones. ATMs are common.
Banks are open from 9:00 till 14:00. Credit cards are widely accepted but may not be in family-run businesses or local neighborhood stores. Personal checks are not widely accepted in Greece, so don't assume that you can use them, unless you have checked with the establishment beforehand. Cashing personal checks at a bank is also not possible.
Whatever the case, you should call your bank to let them know that you are traveling abroad, so they can make a note in your account. Bank security software flags foreign transactions and might block your credit card if large purchases in another country are noticed (a major sign of fraud). Before your departure from home, inform your bank about the country of destination.