There are trams all over the city of Brno, and you can get to almost anywhere by using trams and if not with the combination of busses and trams.
In order to ride trams, you need to have a ticket. Tickets are typically sold at the tabacco store which you can basically find at least one in each block. 10 min ride ticket is 14CZK (which is about .70USD). But I suppose the price differs based on the zone you ride in. I am not too familiar with that yet. But you have to realize the ticket is just so beautiful with all the colors.
If you are using a ticket to ride a tram, you have to get a stamp once you get on. There is a yellow box right next to each door. You just stick in the ticket (arrow facing in). I heard that if you stick it backward, it would not be valid. I also heard that there were undercover inspectors once in a while to catch a "criminal" who would ride free or illegally (meaning no ticket with correct stamp).
And, the locals typically go for a tram pass which I also got after being here for three days and knowing that I will be here for the next how many more months you can guess!
Tram pass is much easier. You have to take your picture and all that, but you can get a pass for a month up to a year. I got one for 3 months. Now I can just ride trams at anytime to anywhere that I want.