There are three main forms of public transit in Budapest: Subway (Metro), buses and trams. Budapest is very well connected this way and you can reach every corner of the city easily.
One thing that might confuse tourists is reading the bus and tram schedules. The way it works is you have to look on the list for the location you’re currently at. Then, you need to add the minutes (Perc) beside it. So for example say the tram leaves on the 20th minute of each hour. You can see that at your location, you need to add 8 minutes for example. So the tram should arrive at the 28th minute of the hour. A little confusing at first, but you’ll get the hang of it.
There are three Metro lines running through Budapest, the M1, M2 and M3.