How to get from Prague airport to Brno?
The trip from Prague airport to Brno is about four hours.
One of the possibilities is Student Agency.
They offer connections with departure directly from the Prague airport (Praha Ruzyne, terminal 1); it takes 4 1/2 hours, which one hour more than usual, but they will take care of you and you need not to think about details.
Student agency is know for their yellow bus so you should recognize it directly. The cost of the ticket from terminal 1 to Brno bus station is 150 CZK (~10 EUR), same for the way back. You can also book the combined flight/bus to Brno ticket with student agency. You can buy the tickets directly at the airport, however without guarantee of a free place. For reservations and more information about the chedule and service email firstname.lastname@example.org. The translated schedule is available here.
The Airport Express is a special bus that connects the Ruzyne Airport with the Holesovice Train Station (Nadrazi Holesovice), which is on line C of the metro. If you need to continue from the Holesovice Station to the Main Train Station (Hlavni Nadrazi), just get on the metro at Nadrazi holesovice and take it for three stops Hlavni Nadrazi (Main Train Station). The Airport Express bus is scheduled to coincide with the arrivals and departures of SuperCity (Pendolino), EuroCity and InterCity trains. A ticket costs 45CZK (2 EUR) and covers the Airport - Holesovice Train Station - Main Train Station route. You have to find your connection from the Prague train station to the Brno train station, go to jizdnirady.idnes.cz and click on the english flag to switch the language, enter "Holesovice/Praha" for Holesovice train station or "Praha" for Prague main station, check "Direct connections only" and search for it.
If you rent a car, just use the GPS or consult google maps.