The currency of Hungary is the Hungarian forint, abbreviated as HUF or Ft. The national currency has been stable for many years and mostly tracks the Euro. At the moment of this writing, one Euro is valued at 324 HUF, and one U.S. dollar at 285 HUF. Thus, if you financially think in terms of these two major currencies, dividing a Hungarian price by 300 should provide you with a rough and yet fairly accurate estimate of the amount. You can also use OANDA to convert financial amounts between Hungarian forints and Euros, U.S. dollars, and many other currencies.
Unless you want to acquire Hungarian banknotes and coins for your numismatic collection, you should be easily able to have a completely cashless visit to Hungary. Only truly tiny shops, e.g., bakeries or public toilets (which do adhere to the venerable tradition of charging small fees for using their facilities), require customers to pay in cash. Restaurants, cafeterias, regular and major shops, taxis, public-transport ticket machines, etc. accept Mastercard and Visa credit card. If a particular vendor does not accept payment by a credit card, you should be easily able to buy an equivalent product or service from another vendor nearby. Note that American Express credit cards are typically not accepted, and checks are not accepted at all.
If you do want Hungarian forints and have not brought them with you from home, you can still acquire them from several booths in the restricted and public areas of the BUD airport, or later in the city (just ask the concierge of your hotel for the location of the closest currency-exchange office).
You can learn more about the Hungarian forint on the VisitBudapest site.