I've gone "Backpacking" twice in Europe now, once in Switzerland, and once through Scandanavia.
I've gone the hostel/train route, and I find this to be rather economical. Granted the places i've travelled to have astronomical costs of living. Try 10 bucks for a Big Mac Meal in Zurich......
Trains are a GREAT way to travel in Europe. The trains actually come on time (to the minute) , don't really break down, have different classes, so you can get sleepers on overnight journeys. If you're travelling across countries a lot, you might want to consider a rail pass. This gives you unlimited rail travel for over regions ( Europe, Scandanavia, whichever you choose), and you pay a little stipend if you want to upgrade your class.
Hostels are clean, safe and very comfortable. It seems that down comforters seems to be pretty much standard in hostels. Most hostels have 1 or 2 single beds in each room, sometimes with a tap/sink, and bathrooms are normally shared. Sometimes, breakfasts of cereal, bread etc are also available.
I find Lonely Planet to be INDISPENSIBLE for selecting hostels and cheap hotels. Their reviews and the rates listed are normally spot on. Don't backpack without your trusty copy of the Lonely Planet.
People are very friendly, especially in the hostels, and remember to ask your host for any reccomendations regarding sights and eats in the locality.
Get an ISIC card,
http://www.isic.org/
this gives you student discounts on just about everything, museums, rail travel, hostels etc.
You might also want to check out
http://www.iyhf.org/home_gb.html
Being a Hostelling International member lets you stay at their well-run hostels, and gives you a discount too.....
With regards to food, and cheap food, check out the local supermarkets. There will normally be a deli section or whatever. This really saved me a ton of money when i travelled through switzerland and Scandanavia.
Most people speak English, or understand English, so it wasn't much of a problem language wise, well, at least in Scandanavia n Switzerland. My friends who have travelled to Greece, Spain, Italy, Germany, etc haven't had much trouble either.
In America, i normally go the priceline/roadtrip method if i travel, mainly due to your abysmal rail system and overdependence on cars.