I've not long come back from Budapest and many local train staff will not speak English but they are very good at writing things down. I speak very limited Hungarian and managed to get around fine.
The metro in Budapest is very easy to follow, colour coded and much simpler than the tube in London.
For time you can point at your watch, for point to indicate time and place and give them a pen to right it down. You can also point at a map for where you want to go or a tube map though the underground stations are shown on all the main maps in Budapest as well as the three main train stations, Keleti, Deli and Nyugati. The word for station is P�lyaudvar.
The trams and buses are more difficult and I'd avoid them if you can take the metro.
Tickets for all three are easy, you can buy a book of 10 to save money and it is one ticket per person per journey.
A journey does not include changing line so you need one ticket for each line on the journey.
At the metro they are stamped before you get to the platform (a machine before the ticket checkers).
Otherwise there are little orange machines on buses and trams you have to stmap your ticket yourself in.
Make sure you follow the rules as if you're caught out it's unlikely the inspectors speak any english and fine is around 6000 HUF.
We found Keleti station very easy when we did a day trip to Vienna, the international ticket office had english speaking staff and everything was well signposted.
Avoid the stations and underground parts outside the metros at night though, keep away from groups of people and don't go alone or look like you might be carrying a lot of money or valuables.