Czech is not an easy language to learn, but making the effort to learn to say Hello, Please and Thank you, really is worth the trouble. Locals will be pleasantly surprised and you might get a smile or a new friend just for trying...
Hello = Dobry den
Please = Prosím
Thank you = De Kuji Vám
Czech is a difficult language. Czech people seem to know that and reward (like Italians- not like often in my homecountries France and Germany) if you try a little bit. As everywhere I try always to learn some words as sign of politeness (Please, Thank you , Hello - very simple : Ahoi, Good bye). But in Prague most people one meets speak English (much better than my Czech) and language is really not a barrier for the visit.
Just as in any country, local people really appreciate when you make an effort to speak their language. Even if it is just the word "hello" or "thank you", so learn a few basic words. They will really value your attempt to learn Czech, and as they are generally very friendly people, will easily help you and share a lot of things with you.
Even if English is the international language, Czech is still theirs so don't expect to have menus in English, or for them to understand everything you say.
It might seem like a very obvious tip to some of you, but trust me, I have witnessed many times tourists complaining and saying "How can they not have a menu in English!!!!"
The first time I went in May 1999, nobody really spoke good English,except in pricey restaurants and I had to speak German (Which is fine by me). When I came back in September 2000, most people had a pretty good command of Anglisky. So the moral of the story is, if you cant handle Czech accented consonants, dont worry :)
I saw some Russian signs around Prague's train & metro stations though, clearly dating back to Communist times... and the metro trains seem to be Moscow Metro rejects, but they still work! :)
Language can be a problem sometimes, especially with older people. Most Czechs older than 20 has some knowledge of Russian (since they learned it in school), but be aware that it is culturally sensitive due to the Soviet occupation of Czechoslovakia, and some people might be offended if you try it. Still, as a last resort and with some polite excuses, it could work.
Czech language is very hard (sometimes even natives don't speak well) so you'll need dictionaries. But some 'usefull' phrases, which you can find in that books, are mostly wrong and they don't exactly mean what they are suppose to. So many young people speak English and German (mostly teenagers and businessmen), a lot of people speak Russian, but don't try to talk to them by using that language. Many people don't like Russians so much because of some historical events so when you'll talk to them in Russian they'll simply walk away or tell you that they don't understand. The best way how to get some informations is to go to one of the many INFO kiosks in downtown or just go to some restaurant and ask the waiter - most of them speak English.
Take the time to learn how to pronounce some basic words. Do not think you can guess at it based on the spelling. Czech is a difficult language to learn and is not pronounced the way it looks. If you learn the basics you will find the people notice it and respect you for it. You can listen to basic words on the web at http://www.locallingo.com/countries/czech_republic/language/