1) Time: It is cheapest to travel in January and February. 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 does not need good weather, just warm and dry clothing. I've traveled around christmas to Toronto, 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 unbelievably cheap in the months of January and February. These are good times to visit Southern Europe; it's warmer there even in winter. I spent 2 weeks in Sicily in March this year. It rained half the time; I was wet and cold but it didn't dampen the trip. It was fantastico!
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 these systems and the establishment of the European Union has made getting aound Europe so much easier. Once you're in Europe, you can almost put your passport away, the Italian trains roll right into France as do the Spanish trains. In Amsterdam, I saw French and German trains. They have the same currency, the euro. It's incredible. Most Europeans speak some English. If you've never been, you've got to go get your passport and make your first trip. Just pick any city, whether it be 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)Accommodations: Since I love train travel, I prefer to stay close to the train stations except in London and Paris where the metro can easily connect me between the trains and the hotels. In London I have 2 aunts that I stay with. In Paris, I like the 3rd and 4Th arrondissement. It is a mixed neighborhood with lots of ethnic eateries. It is busy and lively. Whenever possible I'll forgo the attached bathroom and shower, shaves at least 20 euros off the daily rate. It is a lot with today's exchange rate.
4) Food: Free food; some rooms has breakfast included. It is time with load up on carbs and coffee. Coffee is expensive at cafes. Standing at the bar to partake your food is cheaper than sitting down at a table. In Italy, most mornings would find me drinking my cappuccino and eating my cornetto standing at the bar with all the other Italian men. Finger food is cheap too, an Arancino (fried risotto ball) or a slice of pizza or a pizzete( mini pizza) or a slice or focaccia bread or a ham sandwich or a slice of quiche doesn't cost very much but makes a substantial meal. I do sit down to eat dinner; I don't want to miss out on the incredible European food.