Many carriers operate on czech railways the most common carriers are: Ceske Drahy (National Czech Railways), Regiojet (A low-cost carrier), Leoexpress, Arriva.

Most cities and towns are serviced by Ceske Drahy but you can buy tickets for all carriers in the country via one idos.cz or ceskedrahy.cz by buying "one ticket". 

If travelling from Prague to Southern Morava I recommend Ceske Drahy either the railjet or comfortjet expresses to Breclav (where you will transfer on). They look awesome inside and have beer on tap. If you would like to travel a few dollars cheaper Regiojet does operate trains to Breclav as well and have multiple 'travel classes' to choose from. Low-cost being the cheapest with no service, standard, relax, and business. Read more about them at regiojet.cz