Lots of valuable advice here. You could write a small book using this discussion as a resource.
My first European tour was in 1971 and I rode a bicycle, stayed at youth hostels, ate food bought in markets and stores, and had the very best travel experience of my entire life. I was spending about $4 a day, and almost nothing was pre-planned besides my arrival and departure dates.
In 2012, I traveled solo to Japan and used public transportation, stayed mostly in youth hostels, bought food at 7/11s and other grocery stores and also had a marvelous trip. Thanks to the Inter-Web, all of my travel and lodging was entirely pre-planned, and that's what I'd recommend for today's self-directed traveler.
If you have a flexible schedule, start your travel planning at least six months in advance. You can explore flight options by trying different arrival and departure dates to see which ones give you the lowest price. Once your big flight is booked, you can start looking at inter-city travel options, although many bus and rail lines won't allow you to book more than two months in advance. Budget airlines may also be an option. For example, in May my wife and I traveled inter-city in Spain on Veuling, and the fares were less than we would have paid for a bus.
We usually use TripAdvisor for advance bookings for lodging. We pick a city and the dates we will be there and then sort the hotels and B&Bs by their customer rating. We then look for highly-rated lodging that doesn't cost too much. This was how we found the Ariel House in Dublin and the fine western-style hotels we used recently in Spain. If you want to dig deeper for bargains, you'll need to get some guidebooks and correspond directly with places that don't use the Inter-Web for reservations. (Could be rewarding, but too much work for us.)
Like other commentators, we pack dried, compact food to take with us. Also some candy for quick energy. We walk a lot when we travel so we tend to eat more frequently. Suit yourself, but there's nothing worse than being hungry at 10 p.m in a hotel.
If I'm traveling alone, I will rarely eat at a restaurant, but my wife likes that experience. In the old days this was an easier decision to make because Europe was actually inexpensive. It's not now, and it's hard to find that right combination of price and quality that makes dining out a pleasure. TripAdvisor is also a good resource for finding some options you may enjoy.
One last thought: Be prepared. By that I mean be sure to bring items with you that you may need but which will be difficult to find (or costly) abroad. For example, if I get a cold when traveling, I know what medicine I'll need to deal with my symptoms. I bring it all, ranging from zinc tablets to pure dextromethorphan. Try finding that in Beijing, Nara or Rome.