The simple rule in foreign exchange is this: The more often you exchange currency, the more money you lose. Every time you get money from a bank, the hotel, the ATM, or off your credit card, you will be subject to a retail rate of exchange and a fee. The more often you do this, the more money you lose. So, limiting the number of exchanges you do is the best way to save money.

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[edit] Steps

Notify your domestic bank about your travel plans. There have been many cases where travelers have their card accounts frozen because of "suspicious foreign activity". Your bank means well, but if you don't tell them you might be stranded with no access for cash for several days.
Take as much cash, in the foreign currency, as you feel comfortable carrying and get it before you leave for the airport. Check with your bank to see if they can sell you some currency before you go. Or order cash online.
For any amount you need over the amount you feel comfortable carrying, try to take traveler's cheques in that currency -- not US dollars. If they are not available, plan on using your ATM card.
Be aware that ATM's can be expensive! While it's true that you'll get very competitive rates from ATM's, the fees will come over the top and eat away the savings. It's generally about $5 US from your own bank to use a foreign ATM with about another $3 US equivalent from the foreign bank - although there is no limit to what the foreign bank may charge. And this is on every transaction - no matter the amount!
Understand that credit cards usually get wholesale rates (which is very good) but have fees of 2 - 3% of the US dollar amount of every purchase.
Check if your bank has a sister bank in the country you're visiting; this usually means you won't get charged or charged a smaller fee for withdrawals from said bank.

[edit] Tips

If you use your ATM Card, make sure your PIN is only 4 digits long. Many foreign ATM's won't accept 3, 5, or 6 digit PIN's.
Memorize your PIN by the number. Not by any word it may spell out. Foreign ATM's probably won't have an English alphabet on the key pad.
Try to max out your daily limit. You get the fee regardless of whether or not you withdraw 20 euro or 1,000 euro. So, try to withdraw your daily max so you only have to pay the fee once - then use that cash for as long as you can before returning to the ATM.
Call your bank and see if they will increase your daily withdrawal amount. That way you can get more with each withdrawal for the same fee.
Don't use credit cards at ATM machines. Withdrawals will be treated like a cash advance, plus it will be subject to all the usual fees.

[edit] Warnings

Plan for the worst. Hope for the best.
Take at least one form of back up access to your funds. The people that get in the most trouble are the ones that just take one card or something and then lose it. With no other access to money, it will be hard to get local currency. Your family will most likely have to wire cash to you, which is very, very expensive.