Currency in Slovakia is euro. In major cities banks with ATMs are everywhere, especially in Bratislava, and they are reliable. You get a worse exchange rate exchanging paper money. When they indicate there is no commission it just means the exchange rate is less. Although the rate of exchange can vary, the banks are quite good. There are exchange booths in all of the "downtown" areas of Slovak cities. Exchanging currency with waiters, cab drivers. and similar types is risky because they are likely to take "middle-man" share. Similarly, hotels tend to take a handling fee. Credit cards often have the best exchange rates, but they may not be used everywhere. Payment cards (VISA / VISA Electron, MasterCard / Maestro) are widely accepted in Slovakia in shops, gas stations, restaurants, hotels etc, payment terminals run in online mode requiring the customer to enter PIN code. PIN is not required for VISA PayWave / MasterCard PayPass contactless payments up to 20 Euro.
For taxis etc. you will need small bills. Agree on the rate before pulling away from the curb. Small stores also don't have much change, but there is not problem with large bills in large shops (supermarkets,etc.). If you need help, the banks in cities usually have several English-speaking tellers. etc. Since the departure of the Communists, English has been offered as a study, beginning in the lower elementary school level and many have some understanding of English. In large cities (like Bratislava, Kosice, etc.) most people (esspecialy young) understand and speak English.