Budapest's Ferihegy airport has thankfully emerged from the 1970's brown-veneered chaos of its old terminal, and its shiny new terminal is serviced by over three dozen international airlines. The national carrier Malév Hungarian Airlines operates nonstop flights between Budapest and North America, the Middle East and most European centers. There is no schedule for domestic flights.
The bus is also a popular means of getting to Budapest. There are three main stations, with all international buses and some domestic ones to/from Hungary's south and west arriving at and departing from Népliget bus station. Buses to/from destinations in Hungary east of the capital, leave from the Népstadion bus station. Buses to the Danube bend and parts of the Northern Uplands arrive and leave from bus station Árpád híd. The main carrier is Volánbusz/Eurolines with connections to all major continental European cities. Some of the journeys are long, so take a cushion and avoid flat bottom syndrome.
The Hungarian State Railway (MÁV) links to the European rail network, with different stations handling various destinations. Most international trains arrive at and leave from Keleti station, but always check the station when making bookings. Hungarian trains are clean and punctual but hardly luxurious, so bring along snacks and drinks for longer voyages. For the extravagant traveller, a hydrofoil along the Danube to Vienna is a luxurious possibility.