The Czech Republic is not a large country but has a rich and eventful history. From time immemorial Czechs, Germans, Jews and Slovaks, as well as Italian stonemasons and stucco workers, French tradesmen and deserters from Napoleon’s army have all lived and worked here, all influencing one another. For centuries they jointly cultivated their land, creating works that still command our respect and admiration today. It is thanks to their inventiveness and skill that this small country is graced with hundreds of ancient castles, monasteries and stately mansions, and even entire towns that give the impression of being comprehensive artifacts. The Czech Republic contains a vast of amount of architectural treasure and has beautiful forests and mountains to match.
The Czech Republic, along with its neighbours Slovakia, Austria, Poland and Hungary, is part of Central Europe. Often in Western Europe and North America it is incorrectly referred to as an "Eastern-European" country, and most Czechs are very sensitive about this- many will even pre-empt the ignorance of some foreigners by asking "What part of Europe would you say the Czech Republic is in?" Get on their good side by answering "Central Europe", not Eastern!
Czechs don't appreciate when foreigners incorrectly assume that their country was part of the Soviet Union or the Russian Empire - both definitely false - although it was part of the Soviet Bloc and, until 1918, an Austro-Hungarian territory. Commenting about how "everything is quite cheap here" comes across as condescending about the country's economic status.
If you are knowledgable about the Czechoslovakian communist regime following the second world war, bear in mind that this is still a sensitive issue for many and that it is easy to upset people in discussions on the subject.
Czechs are one of the most atheist people in the world. This is true especially in large Bohemian cities. Don't assume that anyone you do not know believes in God or has a passion for Christianity. Respect that and your religion will also be respected.
Always say hello (Dobrý den) and goodbye (Na shledanou) when you enter and leave a small shop as it is polite.
While dining at a restaurant with a host's family it is customary for THEM to pick up the bill, the opposite of most Western standards. However don't assume they will - but also don't be surprised if they do.
When entering a Czech household, always remove your shoes. Czechs usually wear slippers or sandals when inside a house and never their outdoor shoes. Depending on how traditional the host family are, they may insist you change immediately into house shoes as a hygiene precaution, though this is rare. At the very least they will offer you some to keep your feet warm.
Never mention the Czech towns and places with their former German names, when asking for directions (e.g. referring to Karlsbad instead of Karlovy Vary etc.) or while chatting with the locals. Czechs will be offended and they will regard it as ignorance and a lack of respect towards themselves.
The vast majority of Moravians will take no offence to being called Czechs, and consider themselves to be both. If you are attempting to speak Czech, beware of the complexities and slight differences between the terms Čechy (Bohemia) and Česko (Czechia). Much like a Welshman would raise an eyebrow over his country being called England, using the term Čechy (Bohemia) to refer to the entire Czech Republic may not be appreciated by a Moravian. Since there are no mainstream separatist movements in Moravia, and there is definitely no ethnic conflict, it is infinitely more likely you'll be showered with kisses and plied with alcohol for simply making an attempt to speak Czech.