BY PLANE

Budapest is connected with the major European cities and most of the EU countries by direct flights.
Budapest (Ferihegy) International Airport is the country’s largest airport, located about 16 km southeast of the city centre. Ferihegy has two terminals, Terminal 1 and Terminal 2, often called Ferihegy 1 and Ferihegy 2.
The small, renovated Terminal 1 is used by low-cost airlines.
The more spacious Teminal 2 is divided in two: Terminal 2A is the departure and arrival point of MALÉV Hungarian Airlines and its partner airlines. Terminal 2B hosts most international carriers’ flights.
www.bud.hu

Airport transfers:
Taxi: In order to eliminate unjustified price hikes one sole company, Zóna Taxi won the right to take passengers form Ferihegy Airport. Queue at the taxi stand to receive a written quote for your fare, then pay it when you arrive at your destination. The fare will vary according to your destination, or zone between HUF 3300 – 5100.
www.zonataxi.eu

Minibus service: if you travel alone, consider the Airport Minibus service, a shared taxi operation that collects passengers going in the same directions and will take you to or from anywhere in Budapest for HUF 2990 per person.
www.airportshuttle.hu
Bus: from either Terminal 1 or Terminal 2, the bus takes you to Kőbánya-Kispest station. Buses stop outside the airport terminals. Bus tickets are available in airport terminals for HUF 230, or HUF 300 if you purchase directly from the bus driver.
http://www.bkv.hu/english/home/index.html
Railway: If your flight lands at Terminal 1, there is a quick train service from nearby Ferihegy station direct to Nyugati Station in the centre of Budapest (on the Pest side). (HUF 300)
http://elvira.mav-start.hu/elvira.dll/xslms/uf

BY TRAIN

Due to its ideal location in Central Europe, Budapest is easily reachable by train form other European countries; there are daily connections to/from Austria, Bosnia and Hercegovina, Croatia, Czech Republic, Germany, Greece, Italy, Poland, Romania, Russia, Serbia, Slovakia, Slovenia, Switzerland. Turkey and Ukraine.
http://elvira.mav-start.hu/

BY BUS

Arriving to Budapest by bus is an easy and painless option. Eurolines connects the city to Austria, Belgium, Bulgaria, Czech Republic, Denmark, France, Germany, Great Britain, Greece, Italy, Lithuania, Netherlands, Poland, Romania, Serbia, Slovakia and the Ukraine.
http://www.eurolines.com

Orangways, a low fare bus company offers cheap tickets from and to Austria, Czech Republic, Croatia, Germany, Netherlands, Poland, Serbia, Slovakia and Slovenia.
http://www.orangeways.com/

BY BOAT

There is a scheduled hydrofoil service on the Danube to and from Vienna and Bratislava daily operated by Mahart.
http://www.mahartpassnave.hu/

For futher hints you can visit http://wikitravel.org/en/Budapest