OK, travel to Europe is definitely not cheap but for many, the idea conjures up luxurious vacations that only the privileged few can afford. I studied abroad in Europe back in 2008 and will offer some tips here that will hopefully put traveling to Europe within reach for the average American.
The Plane Ticket
Ideally, you'd want to use Credit Card rewards or Airline Miles to purchase it for little/no cost. However, if you are traveling on short notice or during major holidays, it may not be easy to redeem your rewards for seats. In that case, it's best to look at Kayak, Orbitz, or other travel sites to find the cheapest tickets. Priceline.com is another option if you still have plenty of time before your target departure date but Credit Card rewards are not a viable option.
Please don't be one of those idiotic tourists who simply exchanges all of his dollars for Euros or other currencies at the Airport, Train Station, or other location where tourists gather! Get a VISA debit card from your local bank if you don't already have one and notify them you'll be traveling to Europe and using the card there to withdraw cash. They may charge ATM or even Foreign Exchange fees but it'll still cost you less than paying the scam-like spreads at most foreign exchange dealers and banks.
Get a credit card that doesn't charge any foreign exchange fees. CapitalONE has several cards of that type but lately, many other Credit Card companies have also been following suit. You should always try to pay with your Credit Card first and resort to Cash last.
Although I frown upon exchanging dollars for local currency, it's still best to bring a few hundred dollars as a hedge in case something happens to your ATM and credit cards. If you've traveled abroad previously, bring the local currencies from the other countries you've traveled to and exchange that directly for Euros; keep any Euros you have left after your trip so you can exchange them on your next overseas trip; since each time you exchange money, you'll pay fees and the forex spread, it's best to minimize this.
Beware of pickpockets! Although Europe is safer than the US on average, pickpocketing is likely more of a problem, especially in Southern and Eastern Europe. Consider bringing redundant bank cards, copies of important documents, and extra cash to leave in your hotel room or hostel locker. While being pickpocketed is not a pleasant experience for anyone, it certainly doesn't help that getting replacement cards, passports, and IDs will be a much greater pain abroad, so redundancy is of utmost importance here!
If you're a young single 20-30 something, forget hotels, stay at hostels! They're much cheaper, usually about half the cost of most hotel rooms (not to mention usually located close to the main train stations in every city.) It's also a great way to mingle with other travelers in your age group. Some have expressed concern that sharing a room with dozens of strangers is risky but most hostels have lockers for storage of valuables. You can find reviews and details on hostels and hotels at Hostelworld.com.
Europe has some of the most efficient public transportation systems in the world so why not take advantage of that instead of paying up the wazoo for a taxi or (gasp) a rental car? If you plan to visit multiple countries especially in Northern Europe, consider buying a Eurail pass. Sometimes, the Eurail pass will be less expensive than paying full price for train tickets, but there's an additional bonus: in most cases, you don't even need to buy tickets when switching trains, saving you time and headache. Beware that some trains will require a reservation and you could be fined if you board one without getting a reservation first; these will usually be indicated in the Eurail schedule book.
It's best to check train schedule beforehand if you have Internet access. Deutsche Bahn has a search engine for train schedules throughout continental Europe.
As for getting around in major cities, try to stick with public transportation if possible. Urbanrail.net has some comprehensive guides about subways and metro in various European cities including fares. Buy a daily or weekly unlimited pass if you'll be staying for a while for the convenience and value. However, do keep some cab fare on hand in case you get lost and need a ride back to the hotel or train station.
If you need to go shopping or buy food, it's best to stick to the areas that locals frequent. Check www.wikitravel.org and search your target city. Also keep an eye out for the "Stay Safe" section so that you don't wander into a sketchy neighborhood. If you want cheap phone service, consider installing Skype on your smartphone and using it if Wifi is available.
Many people in major European cities will know at least some basic English but please don't arrogantly expect everyone to have a working knowledge. Even if you're visiting a country where English isn't an official language but is widely spoken (like the Netherlands or most Scandinavian countries), at least learn the basics of their language. Learn how to say "Hello", "Goodbye", "Sorry", and some basic phrases in their language out of politeness. There's plenty of video tutorials on Youtube in this day and age so there are no longer any valid excuses!
Got any other tips that has led to big savings in your overseas trips? Please share in the comments!