The #4 and 6 lines run almost in a circle from Szell Kalman ter in Buda, crossing the Danube, making a half circle in Pest and then crossing again to Buda, the 6 line goes to the Moricz Zsigmond stop, the 4 goes to Uj Buda Kozpont. It is a fun, cheap and relaxing way to visit the city by riding with the locals.

You can take it for the entire trip and back, or hop on another tram at one of the two end stations (the #61) and complete the loop although the 61 is definitely less of a scenic route. On peak hours it is a busy line so you are unlikely to get a seat. Alternatively it is also safe to do it in the evening as you will get a great view of the light on the Parliament when crossing the two bridges or from Gellert Hill. The 6 line runs 0-24 hours.

To ride any tram in Budapest you can buy day or multiple day passes (which start the moment you purchase them) or individual tickets - the same as you use in the subway (do not forget to insert the ticket in the machine as you board the tram). You also can buy a Budapest Card

From 1st of July to end of August there are several contractions. On the lines there are replacement buses. More info:

EU, EEA and Swiss citizens over 65 travel free on all public transport in Hungary.