Go to the "Money Savings Strategies" in the Tips section. Lots of discussions on credit cards, atm's etc there.
I suggest that you just talk to your bank or call the information number on the back of your current credit card to find out how your current card works.
For MasterCard and Visa, I find that there are no extra fees when you use those credit cards. If the price is €10, you will pay "€10" in your credit card statement. There is no separate extra transaction fee. Where the credit card company makes the money is the difference in currency exchange rate, plus the invisible-to-you commission that the credit card company charges to the vendor.
I have used different credit cards back to back on the same day and I find that the currency exchange rates between them are comparable. The currency exchange rate fluctuates minute by minute. Even if you use the same card back to back, you will find that the exchange rate will be different when you get the bill.
Where you can save some money is if you have one of the credit cards that give you a rebate. For example, I have a Tangerine Worldwide MasterCard which gives me back 2% on restaurant meals, groceries and gasoline. I can also substitute one of those vendor classes for hotels. The way that works is that the credit card company is taking some of the money they earn from the invisible-to-you commission that they charge to the vendors and rebate it to you. The same thing applies to any points, airmiles or other bonuses that you may earn on a credit card.
Just as an aside: as a result of a lawsuit, in Canada, vendors now have the right to charge that previously invisible commission back to the credit card user. Not too many vendors are doing it, but there are a few that are starting to do so.
Edit: You should also read up about Dynamic Currency Conversion. All you have to remember is that if any vendor give you a choice of paying in Euros or USD, always choose to pay in Euros. If you opt to pay in USD, there will be a extra currency conversion and possibly an extra transaction fee and you will end up paying much more.