With a passport you are legal to stay in the Czech Republic for 90 days. When you land at the airport you will go through passport control to have your passport stamped. When you go through the passport control do not mention anything about moving to the Czech Republic or teaching English in Prague. You will come to the Czech Republic first as a student in a TEFL course and a tourist and then if you choose to stay long-term you will get a work visa.
Most schools, including TEFL in Prague by Edua Languages, will help you acquire a visa. The process takes quite awhile and you will need the help of the school you will eventually work for. Most schools are accustomed to helping teachers get their visas. If you do not have a visa you need to make sure that you leave the country every 90 days to get a new stamp in your passport. Once that stamp is entered you have another 90 days.
"Prague is a beautiful city and you will have a lot of fun, no matter whether you stay one month or ten years."