The public transport in Brno is provided by DPMB which maintains 13 tram lines, 13 trolley-bus lines and 37 bus lines. During the night the public transport is maintained by 11 night bus lines. If you want to use public transport, buy tickets only for 100+101 zones! If you're staying in Brno for several days, consider buying a 5-day ticket which costs CZK 250. There are several places where you can buy it, but the best one for you is probably the main railway station, where you can buy it at any counter (look for the international ones because they are more likely to speak English).
SMS tickets: DPMB also offers sms tickets. You just need to send the message to a phone number 90206. The code for a 75-minute ticket (CZK 29) is BRNO, BRNOD for an all-day ticket (CZK 99), and BRNO20 for 20-minute ticket (CZK 20). After sending the message, you'll receive a ticket via sms within a few minutes. The service only works for Czech SIM cards. If you don't have one, you can use a mobile app Sejf which is available in AppStore and Google Play.
From Main Railway Station to the Akademy Venue
Take tram No.12, which serves the bus station Zvonařka (tram stop Zvonařka), the bus station at the Grand Hotel (tram stop Hlavní nádraží), and the main railway station (tram stop Hlavní nádraží). From any of those, take tram No.12 to the end station Technologický Park (about 20 minutes). Next, take bus No. 53 (towards Husitská) and get off at the second stop (Podnikatelská).
If you get lost, consider yourself fortunate. That's when the fun begins...have an adventure, enjoy Brno, meet local people, ask for help, learn čeština words (be prepared).