I'm no "expert", but over the past few years, I've learnt a few things about traveling economically and comfortably in Europe. Here are a few rules I try to stick to in order to get the best bang for the buck when traveling around Europe:
1. Be flexible with dates; even a few days of flexibility can save you a lot of money. Search for tickets by entering date ranges instead of very specific dates and times. Check out www.skycanner.net to find the cheapest flights in your date range (there are also other equally good cheap-flight checkers on the web - I just happen to use this one).
2. Be flexible on your destination. Usually, I don't even know which country or city I want to visit; I just say "I want to travel for a few days sometime in September" and see what interests me at the best price.
3. Book early. This is usually a given, but particularly true for trains. I've been able to find low-cost plane tickets just a few days before departure a number of times, but train tickets that could have been purchased for 30 euros if booked 2 months early could cost up to 100 euros just a few days before departure.
4. Consider connection costs for the cheap flights. Often, you only save [for example] 50 euros by taking the low cost airline instead of, say, Air France, but the fact that the low cost airline requires a long trek to and from the departing and destination airports can often make up the difference easily and, even worse, sometimes cost you more.
5. Eat food from the markets. For the first few months of travel throughout Europe we always went to the really nice restaurants and ate wonderfully. But, once we tried buying local food at markets and eating by the many fountains and piazzas throughout Europe, we began to enjoy those (cheap) meals more than the expensive ones. They cost less, you get to try out your French/Spanish/Italian/Whatever at the market, and watch the people and culture walk by as you enjoy the local fare in a Piazza - what more can you ask for?
6. Don't worry. Seriously, I've spent a lot of unnecessary money when I first started traveling Europe simply out of fear of the unknown; I'd stay at the nice "North American Style" hotels, waste money on travelers checks, and eat at restaurants that spoke English. Not only did I waste a lot of money, but I also missed out on a lot of the local culture. So, just don't worry and plunge in as if you are a local.
7. Rent a car. If you're planning on visiting many cities in a single country or region (and you have at least one person travelling with you), car rental can be the best deal. You can rent cars for around 100 euros per week in many parts of Europe so it's not only cheaper than all the train tickets you might otherwise need, but you'll get to see the countryside too - which is where the traditional culture often thrives. One more note: diesel cars are much more economical.
8. The best souvenirs are the memories. Do you really need that Paris bumper sticker?
Some of my thoughts from abroad. You can also have a look at my photos from abroad.