In the last four months my wife, myself, and two of our kids have managed to visit Berlin, Florence, Rome, Venice, Vienna, Budapest, and Prague pretty much on a shoestring budget. We haven't bought a lot of souvenirs to be sure, but we have the pictures and memories. Much of the time, we were on a $100-200 budget a day for 4 people. Here's our formula.
1. First you have to get there. The plane tickets will be the biggest expense. Most will know Orbitz, Expedia, Travelocity, Air Gorilla, Priceline, etc.
2. Eurail is of course ideal for long trips (e.g., to Italy from Munich or from Paris to Stuttgart). Depending on which kind of ticket you get, they are good for several days in the countries you select within a 2 month window. They must be purchased in the States before you go. You do get to travel first class.
Reservations for specific seats are separate and important for the high speed trains (not necessary for the locals). In Italy, they'll fine you if you haven't made a reservation at a train station, even though you have a ticket. In other places you just have to find an seat that isn't reserved. It can cost almost 10 Euros a person sometimes for a reservation, but it saves the hassle of trying to find an open seat--especially one where your family can sit together. There are overnight trains for long hauls but don't do it unless you can reserve a sleeping compartment--trust me.
3. We found buses to be very nice when going into eastern Europe. We took buses from Vienna to Budapest and from Munich to Prague. Eurolines is dependable and has nice buses. We noticed a Eurolines going from Budapest down to Athens and were jealous. You can often make round trips for less than 50 Euros a person on these sorts of bus lines.
4. Twice we rented a car. It can be fairly inexpensive (e.g., 50 some Euros) but you must have a credit card and they will usually block three times the rental amount until the car gets back safely and they get it through the system (which can take some time). As in the States, they may or may not take a debit card.
Also, they often won't let you go to eastern Europe with one. The cheapest will be manual transmission. Diesel ones are of course cheap on gas (you can spend a 100 Euros easily on normal even in a day). I used Orbitz both times. The insurance may be worth it.
5. Know the local deals. The Bayern ticket in Munich can be purchased for less than 30 Euros and will take up to 5 people anywhere in Bavaria and even to Salzburg--6 if two of them are children. In Budapest you can get a two day family ticket for something like 12 Euros (I forget how many Florints).
6. Google maps is awesome. We walked straight from the international bus station to our hostel in Prague following the clear path Google maps worked out for us before we left home. You will almost certainly want a map of any city, though, once you get there. Many hostels give them out for free.
7. For a lot of Americans, the amount of walking the Europeans are used to can be a big adjustment. If you're not prepared to walk a lot and take public transportation, forget about doing it cheaply. There are usually tickets to be bought in the big cities that will allow you to hop on and off any subway, tram, or bus for the day (or several days). Most Americans aren't used to subway and tram charts, but once you get the hang of them they're pretty much the same everywhere in Europe.
Beware of pick pockets, especially in Rome. The subway there is horrible and squashes everyone like a sardine. Keep your wallet in a front pocket or somewhere inaccessible. Don't be loud Americans. Don't expect everyone to do it your kind of normal. Just knowing please and thank you in whatever language will get you miles in better attitudes and service.
By now most know that the best way to get money in a foreign country is at an ATM. Most of the conversion stands are a cheat. If the rate is reasonable (check Google before you go), they'll slap on a commission. If they don't have a commission, the rate may be bad.
Make sure your bank lets you take money from a debit card overseas (not all do) and warn them you're traveling in advance (or they may block it and try to call you at home, which would be unfortunate if you're half way around the world). Also be aware that banks often only let you take out a certain amount of cash each day electronically (e.g., $200). That can be a nice budget... or it can cause serious problems if, as is often the case, no one seems to take credit cards.
1. Housing is a major expenditure if you stay at a normal Western style hotel. Orbitz and those sorts of sites again will find you good deals. Certainly Rick Steve's and the travel books can give suggestions too.
2. With four of us, however, we ended up doing several hostels (Florence, Budapest, Vienna, Prague). There are sites like hostelbookers.com. But just doing a google search "Hostels Prague" and you'll find the roads most traveled. Make sure the hostel will take older people. Usually they want paid in cash up front. But if you have four people, you can usually book a whole room for your family (rather than sharing one). It's en suite.
We had great experiences at the hostels we stayed at in Florence, Vienna, and Prague. The one in Budapest seemed a little dodgy, but we survived intact. They can be noisy. Most of the time the en suite ones have a private bathroom but not always. The breakfast also may not be overwhelming, but you can often get some sort of breakfast included.
We stayed in Prague for about 65 Euros as a family. I think it was something like 45 Euros in Budapest. Vienna and Florence were higher but still well less than 100 a night for four people, I believe.
It's horrible to say but you can always count on McDonalds for a predictably priced meal... and language is usually not a problem. In any language, a family of four can eat at McDonalds for about 25 Euros.
Italian is fairly predictable in price too. A "pizza margarita" or cheese pizza for one or two will cost 6 or 7 Euros. Spaghetti bolognese, napoli, or carbonara will usually be less than 10. Watch how much the drinks cost, even water. 50 Euros for a family of 4 is not surprising.
You'll want to try some local food. Beware the restaurants in the middle of things. The restaurant on the town square will cost you. Find the restaurant on the side alley or a good half a kilometer from the city center. A hostel may very well have advertisements up. We ate at the "Iron Curtain" in Prague following a flier in the hostel at 6 Euros a person (600 Crowns for four of us).
Another big expense are any museums or entrance fees. Plan on it. There are usually lots of things to see wherever you're going... and almost all of them will want their pound of flesh.
Some advice hot off of Prague and the secret to my family's own shoestring tourism.