The best way to get to Tuzla is by car or by bus. You can fly into Sarajevo and drive for about 2 1/2 - 3 hours, but I have to warn you, Bosnian mountains are not for the faint of heart, and this road is full of curves. You can also take a bus from Sarajevo, and the fare will cost you around 10 Bosnian marks (approximatly $4-5). There is a small airport in Tuzla, but to fly into this airport will cost you more than flying to Sarajevo. Another way to get to Tuzla is to fly into Zagreb and drive for about 4 hours, but the road is much better. The train system in Bosnia has been completely destroyed during the war, so don't count on it
The best way to get around Tuzla is by bus that costs 1 mark or by taking a cab that actually costs the same. FYI, if you want to pay only a mark for the cab, it will not take you wherever you want but it goes basically on bus routes and stops at bus stops. In order to actually be taken to your doorstep, you will have to pay a few more marks (actually 5 marks and don't let them charge you more). Tuzla as a city is long but narrow, and a lot of it is in the steep hills. The bus transportation goes in the valley mostly. You can always rent a car and drive, but seriously, if you plan staying in the city only, it's not worth it, since parking is scarce.
If you choose bus and are staying for longer than a month, definitely buy a monthly pass, it will save you money. Also, you can get a schedule of all buses at the kiosques at the bus stations for 1 mark.
Bus is an extremely easy way to get to Tuzla. A bus leaves Zagreb about three times daily, costing 33 KM one way, and buses from Sarajevo (by Centrotrans, Bosnia's most reliable company), leave at 09.30, 10.30, 11.30, 12.30, 13.30, 16.00, 18.00 and 20.00. You can get to Sarajevo by bus from Antwerpen, Berlin (also to Tuzla), Dortmund (also to Tuzla), Frankfurt (also to Tuzla), Hamburg (also to Tuzla), Ljubljana (also to Tuzla), Makarska, Munich (also to Tuzla), Pula (also to Tuzla), Rotterdam, Split (Tuzla as well), Wien and Zagreb (also to Tuzla)
Tuzla has a good city bus system. Tuzla has two zones; a ticket for one zone (generally good to get you to the center from any point other than the center itself) is 1 KM, the one for two zones is 1.5 KM...
Tuzla even has an airport! And the airport has some international flights, to Budapest, Istambul, Zurich, Frankfurt, Vienna and Ljubljana (SLO)... The airport office is very friendly and you can call them at +387 35 814605
While there is an airport in Tuzla, it is not very busy. I get there two ways. You can either fly to Sarajevo. However, that means that you'll have to take either car (which is bad) or bus (which is worse) through the hills to get to Tuzla. This may result in car-sickness. If you fly to Zagreb, you can take the much more confertable route to Tuzla on the highway. However, this is considerably longer, but if you're prone to carsickness, it is the preferable route. Both routes are fairly scenic.
Tuzla has a fairly reliable Public transportation system of buses that go through the city. Because the city is so long, and unless you're really lazy, you'll only need to depend on one line. Just make sure you get on the right bus. The bus is very cheap, however, it can be crowded. If you want to be sure that you'll get to where you want to go, you can take a taxi. Try and aim for the Mercedes