Using the subway: you have to buy tickets in little ticket offices at most of the stations. Good luck with that, they won't speak any English. Ha. Pointing and waving the correct fare might do it.
The trains and trams do get checked and you will be fined if caught without a ticket - for the minimal price of the fare, it's not worth the bother. You can buy a book of tickets if you get lucky with someone to help you - they come in tens and twenties and you punch them on the tram/platform.
It might be possible to buy them at one of the big train stations, where English-speakers may be found. Maybe.
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Well why not try and learn a few words of Hungarian, it's not difficult, or even buy a phrase book. I've never had problems with my very basic Hungarian and a dictionary getting anything, though Hungarians can be a bit slow on the uptake when you mispronounce words. It's not that daunting to buy tickets - the staff don't speak that much English, but they are quite keen to help and "2 single tickets" or "one-day ticket" is widely understood. Don't be put off using the public transport - it's easy to use and efficient.
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Much better than the fiddly tickets are weekly, fortnightly or monthly passes. They are valid on buses, trolleys, underground, trams, suburban and rack and pinnion railways throughout 200 square miles of metropolitan Budapest. The weekly pass is available without a passport photograph. The weekly costs about as much as a single on the London tube.