1) Time of travel: it is cheapest to travel in January and February. The weather may not be the best, you can't enjoy the beautiful vistas of Tuscany or of Provence. If one is visiting museums and architecture, one doesn't need good weather, just warm and dry clothes. I've traveled to Toronto at Christmas, all bundled up; I've gone to the ballet and to the opera while there. I've been in London and Paris at Christmas and the weather was cold but dry. Weather in England is very unpredictable. I have been there over a very wet summer. I've checked the internet for fares and they are unbelievable cheap in January and February. These are good times to visit southern Europe; it is warmer there even in winter.
2) Public transportation: One must definitely make use of the incredible bus, trains and underground systems in Europe. It is the cornerstone of cheap European travel; the vast network of all the systems and with the establishment of the European Union, there's never an easier way to get around. Once you are in Europe, you cn put away your passport, the Italian trains roll right into France, the Spanish trains too. In Amsterdam, I saw French and German trains. They have the same currency, the Euro. It's incredible. Most Europeans speak English to a greater or lesser extent. If you've never been to Europe, go and get your passport now and make your first trip. Just pick any city, whether Paris, London, Madrid or Rome. It might be a little intimidating the first time but there are a plethora of guide books that can instruct you to the minutest detail.
3) Accomodations: Since I love the train system in Europe and use them a lot, I prefer to stay close to the train stations except in London and Paris where the underground system can connect me easily between that hotels and the train stations. In Paris, I like the 3rd and 4th arrondisement. It is a mixed neighborhood with lots of ethnic eateries especially Chinese and Jewish ones. It is busy and lively. Italy, especially Northern Italy is getting very expensive. It is always crowded in Italy. I usually forgo the attached bathroom and shower, it is much cheaper, shaves at least 20 euros off.
4) Food: free food, some rooms has breakfast included, usually the hostels. It is time to load up on carbs and coffee. Coffee is expensive at cafes. Fingerfood sold at cafes can be a cheaper alternative. In Europe, standing at the bar is cheaper than sitting down. So in Italy I stand at the bar to drink my morning cappuccino and eat my cornetto ( a sweet croissant) with a whole bunch of Italian men. It's fun. Sandwiches made at cafes are really tasty, the bread is so good and the ham is incredible. Of course I don't forgo the experience of sitting down to a good meal once in a while, so I could taste some of the local specialties.
Where there is a desire to travel, a way will be found to do it.