Zivnostensky list for teaching
It is quite common for people to use a trade license as a way of finding employment as a teacher.
The process for obtaining a zivnostensky list for a 3rd country national is not an easy process.
The process is complex and if you do not speak Czech it is probable that you would need help dealing with the offices.
If teaching will be your full time method of employment, you visa will be tied you you license and vice versa.
You will need to apply for a zivnostensky list first and then apply for a visa. You have to apply for a visa at a Czech embassy or consulate. That means outside the Czech Republic.
Once you have your visa, you register the visa with the foreign police and then with the trade offices.
As a 3rd country national, you will need to register the trade license with the trade courts.
Once that is done you will be issued with a document that has to go back to the trade register office.
Only then you will finally be given you trade license.
See: How long does it take to get a trade license?