ALSO 10% OF THE MAIN ROADS ARE BEING RENOVATED SO PREPARE YOURSELF FOR TRAFFIC JAMS!!|
Small but important tip - if you are over 65 you travel on trams, buses and rail free (just a reservation fee), but not airlines or special transport like the Children's railway and the lift up to the Fisherman's Bastion in Budapest. If you carry a EU passport all you need to do is show it when asked. Sorry, doesn't apply to non-EU countries. I travel all over Hungary and never pay a penny except for the train reservations.
train infos:www.elvira.hu www.mav.hu
If you can't find the bus timetable, here is a direct link: http://www.menetrendek.hu/cgi-bin/menetrend/html.cgi
Unfortunately it is all in Hungarian, but I think you can figure it out anyway.
For the city transport:
Public transport can be somewhat expensive in Budapest, but it is still cheap compared to Western-European prices :) One single ticket is 230 HUF (cheaper if you buy it in advance and not at the bus driver), ten tickets in a package are 2050 HUF (keep in mind that you should not throw away the "cover" of the ticket package -- it is invalid without it). A three day tourist ticket is 3100 HUF. You can buy a weekly ticket as well for 3600 HUF. Tickets are valid within the boundaries of Budapest and they're valid for the night buses, too. Metro section ticket (valid for 3 stations) is avalaible for 180 HUF. Confusing, huh? :)