Budapest Ferenc Liszt airport is the main gateway to the country, it offers a high number of direct flights to many European cities, and it is little way out of the city. Bus 100E goes from the airport to the centre of the city between 05:00h a.m. and 1:20h a.m. every 10 minutes during the day and every 20 minutes during the mornings and evenings. It stops at Kálvin tér, Astoria and Deák Ferenc tér, all of them within the city centre.
Arriving by train is also an option if you come from a neighbouring country. There are three main train stations in Budapest: Nyugati, Keleti and Déli train station (“pályaudvar” in Hungarian), all of them are connected with metro lines (M2 and M3). The centre of the city (Deák Ferenc tér) can be easily reached with any of those metro lines.
There are two main bus stations if you decide to come by bus, Népliget and Stadion bus stations. Both are on metro lines (M2 and M3), so the centre of the city (Deák Ferenc tér, the main central square) could be easily reached.