Day-to-day interaction with Czechs is not much different than it is with North Americans or other Europeans. In general, Czechs are more reserved in their dealings with foreigners than, say, Greeks or Italians might be. On being introduced, it's common to shake hands; kissing on the cheeks is reserved for family members and close friends. On entering a shop it's usual to say "hello" (Dobrý den) to the shopkeeper, and to say "good-bye" (na shledanou) on leaving. It's considered rude to speak too loudly in public, though this "rule" is often suspended in pubs.
There are no special rules of business etiquette that would be seen as outside the norm in Europe or in North America. Punctuality is valued and seen as a sign of reliability. Meetings will usually begin and end with a firm handshake. Your Czech counterpart is likely to say his or her surname as he shakes your hand for the first time. You can do the same. It's customary during or after a meeting to exchange business cards. Resist the temptation to address someone by his or her first name in the initial meeting. This might be seen as too familiar. At business lunches, feel free to order an alcoholic beverage if you want. Although there's no stigma attached to having a wine or beer "on the job," the younger generation of businesspeople tend to avoid the "three-beer lunch" of the older generation.
One of the best ways to avoid being an Ugly American is to learn a little of the local language. You need not strive for fluency; even just mastering a few basic words and terms is bound to make chatting with the locals more rewarding.
Czech, the official language of the Czech Republic, is a western Slavic language that is nearly identical to Slovak and closely related to Polish. Czechs learn English in schools. Outside of Prague, English comprehension is slightly less common. In the border areas, German is much more common, especially among hotel and restaurant staff. Many people outside of Prague mix English and German haphazardly into a sort of universal foreign language when talking to foreigners.