Trams in Budapest are operated by Budapest Transport Limited. The "backbones" of the tram (and public transportation) network are the following circular lines: #47 #49 from Deak Ferenc ter along Littler Circle, crossing Szabadsag (Liberty) Bridge to South Buda #4 #6 from Moszkva ter (Buda) crossing Margit (Margaret) Bridge, then along Grand Circle, via Petofi Bridge to South Buda #61 closing the 4-6 circle on the Buda side - operating between Moszkva ter and South Buda #1 #1A from Obuda crossing Arpad Bridge and then along Hungaria (Hungary) Circle #3 is the outermost tram ring, from Millenium Underground Railway terminal Mexikoi ut to Pesterzsebet, South Pest.
TICKETS ARE NOT SOLD ON TRAMS, you may get them at most stops from vending machines or from the ticket booths at most metro stations and in major junctions. After boarding, VALIDATE YOUR TICKET. Schedules are always clearly posted under the stop sign - actually, most tram services are frequent during the day. Trams stop at all stops along their routes - but on some vehicles, you may have to open the door for yourself by a door opener button. On such vehicles, don't forget to signal before getting off. Inside tramcars, a list of stops is usually posted, except for times of service changes, detours, disruptions, when only the temporary terminals and service info are shown. Route numbers are clearly displayed at the front and the sides of the tramcars in black or green. Letter "K" (or red script "Kocsiszinbe") means the tram goes to depot: in this case, check where the tram terminates.
Taking a tram is usually faster than any other means of transport (except for trains), as trams run on more or less closed tracks. Sometimes tram services are not operating normally, replacement buses (with yellow-black V sign) stop either at tram stops or at the closest bus stop. Mind that trams are electric vehicles - so they may have fast acceleration. Always hold on when standing, don't get on when the bell is ringing!

Website: http://www.bkv.hu/english/villamos/index.html