There is a direct connection between both cities. Prague's central station is called Praha - hlavní nádraží, in some occasions shortened to Praha - Hl. n. In Budapest you arrive to Budapest Keleti.
The train operator is České Dráhy a.s. (Czech railroads). You can buy tickets on the train station or online. But be careful, when you are buying the ticket online and you are traveling abroad you need to print out the ticket in a size corresponding to a printout on a full A4 sheet.
There are seven direct trains every day, with the first departure leaving as early as 5:52 a.m. after that the trains are going approximately every two hours until 15:52 and the last one leaving at 23:58 - which is an overnight train and you can buy bed there. The journey takes around 7 hours. For more specific times of departure from Prague to Budapest visit the official website of České Dráhy.
The public transport stop is called "Hlavní nádraží" and it is one of the most important stops in the whole city. To get there is easiest to use Metro C, but the station is also served by trams 5, 9, 26 or buses 55, 58. When you are in Budapest and you want to go to city you can use Metro 2 and 4, buses, trams and trolleys you can check on official web of Budapest public transport.
As many documents are written in Czech even English declared, here is the most important vocabulary:
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