EU citizens can stay or visit the Czech Republic indefinitely and without the need for a visa. Citizens of the USA, Canada, New Zealand and Australia can stay for up to 90 days with a passport. Those requiring a visa to visit the Czech Republic must have a passport valid for at least three months longer than the validity of the visa and a return or onward ticket (but usually not checked).
Countries with the Visa Waiver Regime (for ordinary passport holders) – If you are in this group, you can travel to the Czech Republic without the need for a visa for a certain period. If you hold a Government or diplomatic passport, there might be different requirements, so you should contact your nearest Czech embassy for further information. If you are not subject to the Visa Waiver Regime, you need to apply for a Schengen visa (Application for Schengen Visa).
Processing time for issuing tourist Schengen visas varies, and it can take up to 30 days. In general Czech authorities are quite slow, so it is in your own interest to apply well in advance.