From Fedora Project Wiki
How to get from Prague airport to Brno?
By "Student Agency" bus (recommended)
I recommend this way, because the departure is directly from the prague airport (Praha Ruzyne, terminal 1) and the bus crew is speaking English :) 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.