) has a story about phrases that can save you money while travelling in France. It is true that knowing even a smattering of the local language can make a big difference in your comfort level while travelling, and can sometimes result in savings.
I won't attempt to better their list of French phrases, particularly because it's been a while since I travelled in France. French is widely spoken where I live too, but this is North America and so you can generally get by with English in a pinch. That might not be the case in what is sometimes called "le Quebec profond," but it applies in Montreal and, to a lesser extent, in Quebec City.
Phrases that I have found useful in German include "Wieviel kostet dass?"--how much is it? and
"Dass is zu teuer."--that is too expensive. Since German-speaking countries are not places where bargaining is common, the latter phrase may only get you a lower price in a flea market or similar establishment.
Look for items that are "kostenlos" or free, and be on the prowl for the word "billig" or cheap. I once found an inexpensive cafeteria called a Billigteria near the Stefansdom in Vienna. In German restaurants, you may be charged for each piece of bread. On the bright side, your hotel cost will probably include a large and tasty breakfast buffet.
In Italy, say "quanto costa?" to ask the price of something. "E molto caro" indicates that you find the price high. Italian restaurants often have a charge called "pane e coperto" for bread and water. Order "vino di tavola" for table wine, "rosso" for red or "bianco" for white. Beer is "birra," while "acqua di tavola" will procure tap water. Don't expect much in the way of breakfast at an Italian hotel. If it costs extra, it could be worthwhile to seek out a nearby cafe instead.
In Russia, say "stolko sto-it?" to ask a price, and "Eta ochin doroga" to indicate it is too much. Bargaining is possible in Russia, especially at the outdoor markets found near many Metro stations. "Pivo" will procure a beer, while "vina" with the accent on the last syllable is the word for wine, "krasnava" (with the accent on the first syllable) for red and "byelava," also with an accented first syllable, for white. "Voda" should procure water, not to be confused with "vodka." If you order vodka in Russia, you may be asked which variety you like, since there are many.
Of course, all these foreign phrases work best if you can actually understand the answers to questions such as "How much is it?" That means learning your numbers, and practicing listening to native speakers of the language. Listening skills are the part of language learning that I have always found most difficult.
It may not save you money, but if you often find that people ask you for directions, it is worthwhile learning the words for "I don't know" or "I am a tourist" or your particular nationality in the local language. In Russia, "Ne znay you" or "I don't know" said with a shrug covers a lot of situations. The same in French is "Je ne say pa," in German "Ich vice es nicht," and in Italian "No lo so."
If you don't know how to say even this, as I didn't in Sweden and Finland when asked how to get somewhere, an apologetic shrug and "English" may have to serve.