Non-personalized "Bus Plus" card is the best way for you to pay the fare, and it can be acquired at every kiosk on the street. It costs 250 RSD (approx. 2 euro). When you buy it, it is empty and you have to charge it with the amount of money sufficient for at least one ride. The cost of using the public transportation for 90 minutes in Belgrade urban area is 89 RSD (approx. 0,75 euro). When you enter the vehicle you lean your card to the small device on the handle and you will be charged for hour and a half of driving. Feel free to charge your "Bus Plus" card with the amount needed for several rides.
If you want to purchase a daily ticket (1, 3, or 5 days of usage), then you will pay 40 RSD (approx. 0,3 euro) for the card, and additional 250 RSD for 1 day (entireday except 12am to 4am), 750 RSD for 3 days (entire day except 12am to 4am), or 1000 RSD for 5 days (entire day except 12am to 4am). You need to read it on a device each time you enter the vehicle.
Public transportation in Belgrade is in the process of modernization, so you will see all kinds of different "specimens" on the streets, from aged ones still in use to newly acquired modern vehicles. Now, due to the reconstruction of main city streets and squares, many lines are changed so you may find difficult to move around using this kind of transportation. If you're going a little bit further away, you can always grab a taxi.
As you can see on the photo, the war between worlds, the old one and the new one, rages in Belgrade on every corner, on every street, and that's what this city is all about - a constant spiritual battle in the sense of true cosmopolitism.
Getting around the city's principal landmarks is fairly easy by the means of public transportation.