My first stop when seeking cheap flights is Skyscanner.com. This no-frills website is a fast way to determine which European budget airlines serve the route you're eyeing and helps you compare prices.
Although flights may look cheap at first glance, it's important to factor in extra costs, such as the price for getting to and from the airport. Also, since budget airlines don't make much money on your ticket, they look for other ways to pad their profits, such as charging for food and drink, priority boarding, seat reservations, checking bags, and checking in at the airport (instead of online). With planning, a few sacrifices, and light packing, travelers can avoid most of these costs.
One mode of transportation I advise backpackers to steer clear of is a car. While rental prices may look enticing, this is hardly ever the cheapest option. The daily fee may be low, but the extras, such as tolls, gas, and parking, make it far more expensive than it seems. Also, Europe is dotted with automatic speed guns and cameras that will issue a ticket and track you down even across the pond. I know this because my own twentysomething son was photographed speeding and received a $100 ticket, with a $100 service charge tacked on by the rental company.
As for economical accommodations, hostels are still some of the cheapest beds in town. But while being a member of the Hostelling International network used to be the mark of a respectable hostel, that's no longer the case. Standards at most independent hostels are just as high, and they are often more interesting and fun. The best way to find hostels these days is through Hostelworld.com.
Another way to sleep inexpensively is to rent a bed in someone's home. Airbnb.com is a great way to find these, with its extensive list of options ranging from futons in the living room to entire apartments. You can read reviews to make sure it matches what you're looking for, and it's also relatively safe, as cash never changes hands (payment is handled via the website).
Technology is revolutionizing budget travel in other ways as well. During my early trips, travelers would gather at AmExCo offices to share information and collect mail from back home. Today, even cybercafes are becoming dated, as most young travelers carry smartphones, tablets, or laptops, and connect to WiFi in either cafes or hostels.
For communicating with people back home, cellphones are cheap and easy to buy, even for a short trip. But the best deal is to make phone calls via the Internet. If both parties have iPhones and WiFi access, you can enjoy a FaceTime connection across the street or across the ocean for free. Otherwise, Skype is a good, inexpensive standby.
A recent development in Europe is the advent of free walking tours. While the tour technically doesn't cost anything, guides work solely on tips (and they make sure to remind you of that). At first I wasn't hot on these "free" tours, as guides, generally expat students who have memorized a script, emphasize stories over the strictly academic and are known to take liberties with historical events and characters. But they're still enjoyable, and for travelers on a budget, they're an affordable way to get to know a place.
One thing I always encourage young travelers to do is keep a journal (or these days, a blog). As a travel writer and teacher, one of my favorite discoveries is that the journal entries I wrote as a scruffy 20-year-old in 1975 still resonate with the generally much-less-scruffy 20-year-old American exploring Europe in the 21st century. Today the same timeless magic is there - it's just a lot more convenient and comfortable to find it.