The main internetional airport of the Czech Republic is called Prague Václav Havel Airport. It is located about 30 km from the Prague city centre.
Going to the centre is easy, you will get there by buses, which leave the airport regularly. You will see the buses in front of the arrival terminal. Taxi is also available. If you go by bus, take the bus number 119 they leave every 10 minutes from 4:30am to 11:30 pm. Don´t forget to buy a bus ticket.
You can check the train connection from Prague to Karvina online at: www.idos.cz. Choose english version (flag is at the bottom right corner).
Look for time schedule from Praha hl.n. to Karvina hl.n.. Sometime you have to change the train in BohumĂn or other station.