If you live in Tartu, or is going to stay for a while, then you will be happy to know that this city has a good network of buses and microbuses. Check the bus lines map (bussiliinid) to see where is the closer bus stop, and then check the Bus Timetables at the BussiInfo site.
So, how can I use the buses? If you pick the yellow microbus (Automen Ekspressbussid), then you pay 15 eek to the driver when you enter and that's all. But if you are taking the city GO buses, it gets a little bit more interesting! Randomly red cars from private security enters the bus checking if you have a valid ticket. If you don't, you will be eligible for a 600 eek fine!
So see below how you can buy your ticket and don't travel like a rabbit (Jänes, like the estonians say for the one who travels without paying).
You can buy your tickets in the bus with the bus driver (16 eek in cash for 1h trip), or by little one-trip punchable bus tickets (13 eek, 8 for students) in advance at the R-kiosks (just remember to punch them when you enter the bus. You can also buy a 10 bus tickets pack, with great discount (100 eek, 10 eek each, way cheaper)!
If you need to use more than one bus trip, then you can get the paper one-day ticket, 30-days ticket, or even a 90-days ticket. You don't need to punch them, they are dated in the R-kiosk when you buy it. More info about the prices (in estonian) at the nice City of Tartu website .
But of course, in Estonia, an electronic solution is also available: Id Pilet . With your Estonian ID, you can buy your hour ticket, day ticket, 30 days ticket or 90 days ticket from Internet or mobile phone, and its cheaper than the paper version! I've been told that some people try to buy them when they see the ticket fiscals car in the bus stop, but I haven't seen that yet :)
Just be careful because every season the bus time tables changes, and sometimes some roads are in repair, making some bus lines changes as well.
Well, for a city where you can get from the city center to the city limits in half an hour walking, maybe its better to walk. What do you say?