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
A very useful and easy app to use to figure out the trains in Czech Republic, is the app IDOS! It shows you all the trains and buses on one singular app. You just put in where you are (DO NOT USE THE MY LOCATION FEATURE as it will try and get you to the train station as well and won't give you all the trains), where you want to go, and what time you want to leave around.
The app icon looks like a train on tracks from the front, with a red ticket next to it.
You can buy tickets for multiple companies within the app as well. Though