Listen to Hal:
Before the end of World War I, the regions were Bohemia, Moravia, Slovakia, etc. (I'm sure there are a couple more.) Czechoslovakia came into existence after World War I. The Czech Republic came into existence after "The Gentle Revolution" in 1993 when Slovakia became a separate nation.
You will see posts where authors correct those who use the terms incorrectly. When you create your family tree, we encourage you to use the correct geographical entity, not Czechoslovakia, since your ancestors came over before it came into existence.
To complicate matters, the US censuses can be somewhat inaccurate. For the same family, in one census, it says Bohemia. In the next one, it's Moravia, in another the country is crossed out and someone writes in Austria or Austria Hungary. Then in the 1920 census, the respondent correctly says "born in Bohemia" and it is crossed out and Czechoslovakia written in. (Poland is equally confusing; some regions changed hands 3 or 4 times, and it is different each census, too.) The moral of this story is that you cannot count on using the country in your search.
You will find out that history is finally fun; you do not have to answer questions the way a teacher wants you to, and can study what you want and draw your own conclusions. History was my weakest subject in school, but now I really enjoy it.