If you are new to Brno or planning to come to Brno in near future there is one you need not worry about, that is transportation. I have not spent too much time in Brno either to be an expert in most recommendations. For sure one thing I do not have an issue here in Brno is with regard to travelling within the city.
Like in other cities of Europe there is good connectivity, service run by DPMB. Tram lines and bus lines cut through all part of the city. One can take a ticket from the vending machine in many tram station or sending a SMS with a Cech Republic mobile operator SIM card or from the driver of tram or bus. Buying ticket could get expensive if you are frequent traveller/changing lines, so there is another option to purchase monthly/quarterly/half-yearly/annual pass.
To purchase a travel pass go to Hlinky 64/151, Pisárky, 603 00 BRNO with a photograph of yours and an id card. If you are an expat or tourist to Brno then carry your passport/resident permit.
If you are sceptical about going to office due to language issues do not worry. It is not difficult at all. At the office counter they will give you a form, you give your passport for verification and photograph, pay the amount corresponding to the travel pass duration and you are all set.
If you want to buy the pass online then go to the website of DPMB and register yourself. Keep a passport size photo ready on your computer and you would need a wireless enabled bank card for payment. Why a wireless enabled bank card is because when the ticket controller comes for checking during travel you just need to tap the bank card on the device for verification.
To know about the routes and the bus number or tram number to take you could install DPMBInfo app (if you are android phone user) on your mobile. It also contains latest information and many more details which would be useful.
The tram and bus service runs as per schedule so plan your journey accordingly. Don’t worry if it is late in the night, there is night service across (only buses) and there is no extra fare.
Apart from DPMB, you could use Liftago taxi service and many city taxi service. They are definitely expensive.
Brno is connected to major cities like Vienna and Prague via train service run by Ceske Drahy.
Happy touring across the city.